Someone who is "on the rebound," or recently out of a serious dating relationship, is popularly believed to be psychologically incapable of making reasonable decisions regarding suitable partners due to emotional neediness, lingering feelings towards the old partner, or unresolved problems from the previous relationship. Rebound relationships are believed to be short-lived due to one partner's emotional instability and desire to distract themselves from a painful breakup, and those emerging from serious relationships are often advised to avoid serious dating until their tumultuous emotions have calmed.
In dating, "Julie is on the rebound," means Julie has recently broken up with her long-term partner, while "Mike is Julie's rebound" means that Mike dates Julie during her rebound period.