Usually the animations you make in Blender have little or no interactivity - you set them up in advance and then play them or render them but the only interactivity while they play is that you can change your viewpoint. The Game Engine gives you much more interactivity, so that you can, for example, control a character's movements in real time, just like in a video game (or in SketchyPhysics, if you know that SketchUp plugin). This page gives a brief introduction to Blender's game engine.
Watch the 12 minute YouTube video lower down this page which is from the Blender Nerd website, . The video shows you how to:
- switch into game mode
- give a cube dynamic physics properties
- run (play) your game
- display the logic editor
- create new sensors, controllers and actuators, adjust their settings and link them together
- control the motion of a cube over a plane, and make the cube jump
- how to orient the camera correctly (Alt+R to reset the rotation, then R90, then RY-90
- how to make the camera follow the cube
Note that the (slightly drunk?) presenter forgets to mention that to exit play mode you should press Escape. Also, I suggest you might want to start by giving the vertical sides of the cube different colors so that you can know where the 'front' of the cube is as you drive it around.
Be sure to watch the video in 720p resolution.