Irasshaimase is a Japanese word meaning "Welcome!" that is most often heard shouted vaguely in your direction at disturbingly high volume whenever you enter a store or restaurant or even seem to be approaching a stall or stand. Wandering around a supermarket, you may also hear the employees muttering this to themselves even when nobody is around, apparently out of pure force of habit.
To be pedantic for a moment, "irasshaimase" is the polite humble imperative of "iru," which means "to be." Thus, shopkeepers are politely and humbly requesting that you "be" in their establishment when they scream this at the top of their lungs.
A final word of warning - because "irasshaimase" is both polite and humble, you are advised to avoid using this on friends and casual acquaintances, or else risk sounding ridiculous, or even feminine (bad if you are a guy). If the occasion calls for formality, the slightly shorter and thus slightly more casual "irasshai" may be best, and many times you may be better off using "yokoso" or some other alternative.