There are several possible explanations circulating on forums throughout the web. One of the most popular ones is that like bleach purifies clothes, Ichigo will purify the world from evil spirits. Or it could simply be a reference to the fact that many people in the story believed at first that Ichigo's hair was 'bleached' (dyed), however it was his natural hair color (oddly enough, as he, like most other characters, is Japanese).
During an interview for Shonen Jump, Tite Kubo said that he named the manga series 'Bleach' because the story uses a lot of the colour black in it. Calling the manga 'Black' would be too boring so he decided to call it 'Bleach' instead, since bleach is white and white is the opposite of black.
This question was asked on the wiki: Bleach Wiki.