"Shitsurei shimasu" literally means "Let me allow to bother you." You can use this phrase when you have to behave a little impolitely or inappropriately in public/business situation.
-enter someone else's office or meeting room
-leave the office after a work day
-leave from someone after meeting
-pass in front of other audience in theater
-need to touch someone's body (used by hair-stylists, cloth shop sales assistants, airport security staff etc.)
and so on.
"Shitsurei shimasu" is a quite polite expression, but if you want to be more polite, you can say "Shitsurei itashimasu."