You know those things. Takes place in the past. Invites lavish production values like art direction and costumes — and usually cinematography while you're at it. It's kind of hard to define what defines "period" films per se — something that took place a decade ago could count, technically, but period pieces set in the very recent past are rare unless it's to poke fun at the era in question. Big budget period pieces are often dramas, frequently big epic ones, and take place at least thirty years ago - because any period of time greater than 25 years tends to shade into "when your parents were kids", which would obviously be pretty unrecognizable to you.
Very often Oscar Bait. Sometimes it's based on literature that was contemporary when published, but feels like a purposeful attempt to recapture that era for new audiences. (Adaptations of the Brontë sisters, Jane Austen, or Charles Dickens are especially common.) Useful if the period predates a Trope Breaker.
The BBC makes a lot of these, and PBS imports them wholesale. The BBC have sometimes even been accused of "falling back" on costume dramas when they've gotten into trouble for something or when the licence renewal is coming up and they need to show they can do some "proper" drama. That said, they're very good at making them: they usually garner a lot of praise, and the end result is packaged into box sets for sale during PBS pledge drives. As a side effect of their decades of Period Piece production, The BBC has accumulated a vast stockpile of costumes and expertise, which is occasionally raided by sister shows such as Doctor Who when they decide to do a historical episode.
There's no real need for examples. Just about any show set in the past counts. You'd know one if you saw one. Some Tropers restrict this trope to "any show set in the past that could have been set in the present", but that ignores the fact that it's impossible for most period pieces to be set in the present day because the plot and the characters' motivations would be nonsensical due to Values Dissonance. For example, setting Pride and Prejudice in the present day as is would make the crisis (Wickham's eloping with Lydia) seem inconsequential and the reaction silly, since the entire point of the crisis is that if Lydia doesn't marry Wickham and clear the family name, the rest of the sisters will end up as impoverished old maids because no gentleman will marry them. That's the way life was in 1812. (Even further proved that, in The Lizzie Bennet Diaries, they had to change Lydia's scandal to make the plotline work). Tech Marches On can also lead to a period setting; in Super 8 the titular media's three-day minimum turnaround time was a load-bearing Plot Point that meant the characters working in instantly-viewable digital video simply wouldn't serve the narrative.
On the other end of the scale, if the story would make more sense set in the present because the characters exhibit modern values that's Purely Aesthetic Era; if it's set around a specific event in the recent past, enough that the lack of distance from the era leads to sloppy set mistakes it's Present-Day Past.