Salam!
V + 고 있다 is used to express a continuing action or a process.
고 is connecting particle
있다 means "exist, stay, remain"
살고 있다 literally means "continue to live "
그는 여기 살고 있어요 means "He have lived here until now and He will live here tomorrow"
그는 여기 살아요 means "He lives here at this time. It is uncertain either he lived here yesterday or he will live here tomorrow"