When two people each have something of their own, it's their respective thing. In a boxing match, the opponents each start in their respective or individual corners.
Respective comes from the Latin respectivus meaning "having regard for." Everyone has regard for what's respectively theirs. We have respective opinions, respective responsibilities, respective anxieties. It's basically another word for individual. Each of a set of twins probably has his respective bed, even though they might share a bedroom together.