I want to expand a little...
The main sequence is a track in a diagram called Hertzsprung-Russell diagram (HR diagram), and is called "main" beacuse stars pass the major part of their lifes in this track. Stars come to the main sequence from another track called (guess what?) pre-main sequence. Stars that have just arrived from the pre-main sequence to the main sequence are called Zero Age Main sequence stars, and are stars that begin to fuse hydrogen in its nucleus.
Stars let the main sequence through various "exit doors". Some take the Giant branch, others more massive take the Supergiant branch, while others (red dwarfs) end up in the White Dwarf region