The Overworld is the "main" dimension in minecraft. It's where you start the game, and it has all the standard minecraft scenery.
The Nether, Minecraft's "hell" dimension, is filled with lakes of lava, lavafalls, netherrack blocks, and strange creatures. In order to get there, you must construct a nether portal.
The End is Minecraft's endgame dimension of stark, eerie floating islands. To get there, you must find an end portal in a stronghold, and repair it with eyes of ender. To get back to the Overworld, you must defeat the ender dragon who live in the End.