Cloud is part of a love triangle, torn between Tifa and Aerith. He has known Tifa since childhood, and actually joined SOLDIER to impress her. Tifa shares the same hidden feelings, and perhaps they would have gotten together, if not for Aerith.
Aerith "hires" Cloud as her bodyguard, in exchange for a date, and they grow close from there on. Although an event prevents them from getting together formally, it is assumed that they would have.
I happen to share a different opinion; that Aerith sucks. In my fan fics, Cloud and Tifa get together, as I think it should be.