Very basic basics: it's a computer game where you move around and interact in a virtual, 3D world. Every world is nearly unique with landforms, oceans, jungles, plains, villages, cave systems, etc. You can build things, dig things out, find minerals and craft with them, farm livestock, fight zombies or each other, build automated systems using sensors and blocks that react to signals.
There are various modes from creative mode with flying, infinite resources, and no monsters, all the way up to a desperately difficult survival game with lots of powerful monsters. It's possible to join games with others in your own home network or over the internet. The pocket edition is almost the same but not compatible with the computer version.
It is also possible to 'mod' the game yourself to create your own personal version with different rules, animals, or blocks. We haven't gone there.
