From level 1-1 of Super Mario Bros, an antepiece followed by the associated setpiece. It's difficult to jump up the stairs without falling into the pit. The first is a low-stakes version of the second, existing to give you a heads-up about the potential danger.
Say a video game developer wants you to do some interesting, complex, impressive thing; a puzzle or something. But they don't want to be too hard on you - so they make the challenge as approachable as they possibly can, as approachable as it can be without them having to compromise the coolness of the idea. But what if this isn't enough? What if lots of playtesters are still getting stuck on their cool setpiece, and at this point it cannot be made any simpler for them - what can the game designer do to allow them to keep their cool thing, but not have to frustrate players? This is where an "antepiece" comes in handy.
An antepiece is a seemingly-innocuous task that precedes a great-big-difficult-challenge, and gives you subtle hints about how you should deal with the great-big-challenge that you're about to confront. The picture from Super Mario Bros.
on the right gives the best idea of what we're talking about here: a challenge that is paired with an "version" of the same challenge that is in some way "easier". In this case, the challenge is "jump up a staircase and land on the top step. You must maintain enough control that you don't overjump and end up in the pit". That is what you MUST do to get past the staircase on the right. Getting past the one on the left is easier, because you're allowed to fall in the pit - but being otherwise the similar it's a stern warning about the second, a practice version. Example taken from this webpage: 
In architecture, a small room that acts as an entry point to a larger room is called an antechamber. An antepiece is an antechamber for a video game setpiece
. Crucially, all antepieces are VERY easy/nonthreatening, often things the player simply breezes past and may not give a second conscious thought to.
This is a form of Instructive Level Design
, allowing a game to maintain a state of "Show, Don't Tell
"; instead of the game explaining through text or voice how something will work, the player experiences the thing quite directly. Compare with Training Dummy
. Contrast with Recurring Boss
, where you have a boss or maybe a certain set of challenges that are related, with some kind of quantitative change. The change from an antepiece to a setpiece is different to that though, it's a qualitative change - the antepiece won't have anything resembling the same challenge involved in the setpiece it is paired with.
developers, who use antepieces a lot, have things called "mechanic reminders", which are a subset of antepieces. An antepiece may tell you something quite new, while a mechanic reminder simply reminds.
- Portal has a few of these. Test chamber ten is a three section chamber. The second and third sections are about throwing yourself down a pit into a portal at the bottom and flying out of a wall. But the FIRST section of chamber ten is barely a puzzle at all; it's just a panel and a staircase. All the player has to do to keep moving is make a portal anywhere and go into it. But it introduces a structure that is going to be immediately built upon to get more thoughtful puzzles.
- In the developer commentary of Portal Two, they mention instructive level design about bombs. The final battle of the game requires creative use of taking the bombs the boss throws and portalling them back. However, the bombs show up one level before, ejected out of a pipe in a controlled repetitive fashion, so the player can get used to their trajectory.
- The Megaman games have their share of antepieces. Egoraptor describes a bunch of them in this video  - an obvious example is the flicky platforms that turn whenever they hit a gap in their line. The first flicky platform is an antepiece - when it doesn't do any flicking at all, so being on it is trivial. It clear, when you see a nearby platform flick, that the flick is caused by a gap in the line.
- Super Mario Bros.:
- Super Mario Bros. contains many, with the first described above. 
- Super Mario Land also has one or two antepieces. In this image  you can see the third boss on the far right, who tries to crush you by throwing bouncing stones. On the far left, a positioned just before you will encounter him, you can see one of those bouncing stones. That anticipatory stone presents no real danger, because it only bounces beneath the question boxes, which you can jump onto. The purpose of the stone is to warn you about what is ahead and maybe give you the opportunity to practice dodging and jumping on them in an enclosed environment.
- Super Mario Galaxy 2 features a level that involves Yoshi spitting Bullet Bills at glass domes to break them. The concept is introduced with Bullet Bills firing in a slow, predictable pattern, and the glass dome being stationary. Later, the Bullet Bills are aimed, and Yoshi must spit out the Bullet Bills while on a moving platform. This leads up to fighting a boss using the same techniques, while in a hectic enviroment.
- Super Mario 3D World has the Hisstocrat boss, which requires you to climb up his fellow snake monsters with the Cat Suit so you can jump from them onto his head. Before all this, there are stone pillars in non-boss levels that resemble the snake monsters and have arrows up their bellies that encourage you to climb up them, foreshadowing the boss fight.
- In an underground scene in World 3 of Braid, there is a puzzle about complex interactions between keys and doors, some of which are affected by your power, some of which aren't. There are two puzzle pieces: getting the first one can be done without thought or understanding, there are only two doors and one key. But solving the three-door-two-key puzzle that follows requires reflecting on the simpler situation. A picture can be seen here
- VVVVVV has antepieces. Here  is an easy example. The player moves from left to right through it. When they go through one of those lines, the direction of gravity is reversed. To get through the red room they can just hold right. the next room is much trickier but the player has a pattern in mind to help them.
- The Half-Life games have a few examples. I'll describe an early physics puzzle in Half-Life 2. There are a bunch of barnacles on the ceiling with their tongues hanging down. There's an explosive barrel near you. If you pass the barrel to a tongue, the barrel will be pulled up to the ceiling, and you can shoot it, and it will explode near the barnacles, and they will all die in a satisfying way. BUT moving objects around and collaborating with a tongue is a pretty elaborate plan to be expected in an FPS...
So, just prior to entering this room, there's a part where you must elbow your way through a bunch of (nonexplosive) barrels. When you do this, one of them will fall down a slope and slide into a small, non-threatening group of barnacles where, in full view of the player, it will be picked up by a tongue. The player now knows barnacle tongues pick up barrels upon touching them. This is described in more detail, with pictures, half way through this article: 
- anna anthropy used antepieces in Mighty Jill Off. There is a particular one-screen challenge which contains three individual, challenging, movements. Each movement has previously been presented to the player in isolation. This gif shows the room and the three previous parts of the game. anna describes the whole thing in this lecture: 
- In the first Metroid and in Metroid Zero Mission, there is a difficult shaft you must climb at the very end. At the start of this last level, there is a similar shaft with wider platforms, where you are punished much less for falling.
- There is a level in Flower which sets up some challenges that try to convince the player to move in a spiral for a later challenge. First you move in a circle around some haystacks, then in a area-filling wavy curve on a flowerbed.
- The puzzle game Music of the Spheres uses an antepiece towards the end of the game. The final puzzle of the game involves a strategy that will allows you to detect the movement of an off-screen enemy. The levels before that final puzzle are very similar in structure to it, except that you CAN see the place that will later be hidden from you. This allows you to get accustomed to the structure of the challenge before the challenging part is actually introduced. Other examples of antepieces can be seen at the bottom of this article: ◊
- The mid-eighties puzzle game Pitman (aka 'Catrap') has very clear antepieces. In this image  the left puzzle is the antepiece for the right one.
- According to the designer, speaking on twitter, Miegakure uses antepieces.
- Stage 5-8 of God Hand seems to be an interesting antepiece for the very difficult boss fight that is stage 5-9. The boss is an enormous entity compared with previous enemies, a ball-shaped thing that is very tall and wide, which is intimidating because your area of attack is really kinda small. You NEED some training, something to get you comfortable with the idea of an object so big that it requires several side-dodges to get away from. So they have you push a large metal ball the same size as the boss up a hill. You learn "hey, I don't have to be DIRECTLY in front of this thing to kick it!", for example.
Interesting note: God Hand is meant to be oh-so-very-very-harsh. But, as with Megaman, the designers turn out to be quite considerate when you examine their work closely.
- Mystery Quest for the Nintendo Entertainment System has a simple pit for unwary players to fall into. This pit is harmless, but requires Wall Jumping skills to get out of. This prepares for a mandatory Wall Jump later on.