Ender's Game and the Ender's Shadow series take place in an Earth with very advanced military and space technology, but otherwise is identical to Earth (technology-wise, the political situation is different). At first I found it strange that a world could be so advanced in the areas of warfare and space travel, but otherwise be very similar to today's technology. Then I realized; the Buggers had attacked Earth and killed a lot of people, causing the first Bugger War, which led to the second Bugger War. Earth has continuously been at war with an alien species that is a known threat, so of course they would put heavy funding into warfare and space travel so we could take the fight to their turf. With such a heavy focus on the Bugger Wars, technology on Earth would have stagnated until the threat was over. This is a believably realistic evolution of technology on an Earth attacked by an alien presence- Gneissisnice.
Also most of the new technology that earth has gravity manipulation and even hyperspace (to an extent (the Ansible)) and especially The Little Doctor are all things military brass would very much like.
Science is just starting to find out that people are really, really good at games. (No, really. Give Science a break, she has a lot to work on.) Why is this important? In the future, they definitely will have learned that people learn best via play.
Earlier on, Petra tells that Ender that although the teachers gave an explanation for the artificial gravity system, it contains holes and contradictions. From the deceiving and untrustworthy behavior of the teachers, Petra prompted: "Our teachers are our enemies." Later, when Ender first encounters Mazer Rackham, it folds back onto itself, this time as, "Our enemies are our teachers!"
Mazer: I surprised you once, Ender Wiggin. Why didn't you destroy me immediately afterward? Just because I looked peaceful? Stupid. You have learned nothing. You have never had a teacher.
Ender (angry) : I have had too many teachers, how was I supposed to know you'd turn out to be a-
Mazer (whispering) : An enemy, Ender Wiggin. I am your enemy, the first one you've ever had who was smarter than you. There is no teacher but the enemy.
It bothered me at first that Peter ended up this beloved Hegemon after being such a monster as a child. Yes, Ender admits that he probably saw Peter as worse that he really is, but we see directly how Peter acts. Making very specific threats about how you're going to get away with murdering your siblings is not normal behavior. Then I heard a theory that low-level symptoms of sociopathy, if combined with good self-control and high intelligence, can actually be very useful for successful business or political leaders. The ability to lay off thousands of workers or order soldiers into battle without hesitation or remorse can actually make a ruler much more effective. Once Peter learned self-control, his sociopathy is part of what made him a great leader.
It goes further than that. Peter is humanity in a microcosm, with the rest of humanity as the buggers. As he learns to work with the rest of the world, Ender is teaching humanity how to deal with the buggers. In both cases, the mismatch caused violence. He's just lucky enough to figure it out *before* killing everyone.
When Valentine visits Ender at the lake, she notices a wasp as they lay together on the raft. She chooses not to fear it, as she normally would. Instead, she desires to live peacefully along side it. At this moment, Ender preemptively destroys the creature. This is a direct parallel for the Buggers. We could have chosen to live in peace. Instead, Ender brutally extinguishes them.
Ender : These are a nasty breed, they sting you without [provocation]
In the film, during Bonzo's fight against Ender he slips and cracks his skull against the shower threshhold. Ender then starts calling for help. Bonzo had just sent his two thugs to watch the door, so why didn't they come upon hearing him? Possibly because they assumed Ender was losing and was calling for someone to save him.
As someone who knows about military training, the way the training worked came off to me at first as...very wrong. Making sure Ender was constantly isolated, shifting him to a different team whenever he started to earn one team's respect, insulting his teammates so they would hate him... sure, strife creates strength, but it also creates distrust, and distrust creates disloyalty. It all makes more sense when you take the ending into consideration. The military never wanted a leader who would make calm and rational decisions. They wanted a psychopath who would pick out a goal and pursue it coldly, with no thought given to cost or consquences - the sort of person who would annihilate an entire planet all in the name of "winning the game." They mention Ender being the next Napoleon or the next Julius Caesar, but what they really wanted him to be was more like the next Vlad The Impaler.
Graff gives Bean a spool of rounded nanowire to use as a tool. He can then utilize that wire to spin around stars and accelerate. Why is this so important? Because what Bean's effectively using is a crude metaphor for a gravity assist, where a ship 'skips off' a planet or star's gravity well to accelerate itself rapidly and efficiently.