"Irasshaimase!" is an honoriffic
expression welcoming someone somewhere (usually into a place of business). It shows respect toward the
performer of its action (the customer) by honoring them as opposed to humbling
the speaker.
The plain form of the word itself is irassharu, and is an exalted form of several verbs including kuru (to come), iku (to go), and iru(for animate objects to exist).