It refers to service industry it is a quite a large category. You could break it down to several smaller industries Healthcare industry is largely a service industry since you deal with patience face to face. Restaurant, Tourist, and I am sure that there are many more.

A career in service historically meant that a person would be working as a domestic servant for a wealthy person or family, often for the aristocracy. It would include working as a maid, a cook or a butler, for example. In modern times it is more likely to refer to someone working as a waiter or waitress or something similar. More common in recent times would be "a career in the service industry" rather than "a career in service".