There are a few of variations of the usage of the expression 'big up' which are worth mentioning, all of which broadly retain the meanings of tribute and respect described by knifegirl.
"Big up your chest!" is used often to address both men and women and means, "Be proud of yourself, you've done well!". It probably refers to puffing out the chest, a common signifier of pride.
"Big up your vest!" is an amusing variation that I have only ever heard addressed to women. It has much the same meaning, but also implies attractiveness.
"Big up your belly!" is a usage that I've only heard used very occasionally, again only addressed to women. I'm guessing from the context that it is very similar in meaning to "Big up your vest".
These expressions were used frequently in the British underground club-music scene and on pirate radio stations, particularly those playing drum'n'bass and the British versions of garage and house music. They subsequently became more widely used, and are still popular at the time of writing.