I'm from the US and I've gathered that Brits use it to mean "goodbye" or "thank you." (Someone correct me if I'm wrong!) In the US we only use "Cheers!" when clinking our glasses together when we're about to enjoy an alcoholic beverage with our friends. :)

As Alecia has explained, it's not a common expression for the Americans. They favour expressions like, "See you later, mate!" "Later, dude!" "See ya!" Generally, it is understood by the Brits and Australians, though. So don't be afraid to say that to an Australian ^^

"Cheers" means "thank you" in british english. It is used during friendly/informal speech. Surprisingly, more men use this word than women in UK. I have not come across any woman using this yet, and I have no habit of using that word either for "thank you". We also use it for clinking our glasses in celebration like the americans.