Minikits are Cube-shaped canisters, painted black and slightly grey with an antenna and a Bat-Symbol in the middle.
There are 10 in each level (most require a Free-play character and certain ability to get) and when you get them all, you will get extra Studs at the end of the level. Then a statue in will appear either the Villan trophy room (Found in the Arkham Asylum hub) or Wayne Manor (Found in the Batcave hub) depending on whether the level is a villian or hero level.
If you have some but not all minikits in a level, the statue can still be viewed but cannot be rotated. The name will not show and the statue will have missing parts. In the portable version of the game, when you collect all Minikits in the Villain hunt you get Ra's al Ghul.
In this game, collect all the Minikits of a level give you a Minikit Vehicle that can be activated either in the Batcave or nearby Bat computer terminals. Also, collecting them all will give you extra Studs at the end of the level. The vehicles will either be miniature versions of full-size vehicles you can get normally, or mini-vehicles of playable characters in the game.