Being on the rebound is the result of being dumped. She is looking for a new relationship to fill the void left when she was dumped. Anyone she hooks up with may be disappointed because she is not sincere in her reasons for starting a new relationship, she will take just about anyone at that point in time. If the new boyfriend is looking for a lasting relationship he would need to wait until she gets over the last one. Many people who are on the rebound go through a series of relationships that have little meaning for them in order to overcome the negative feelings left from being dumped.
I am quoting from Cambridge Dicitionary Online: "five months after Nick had left her, she married another man on the rebound."
As far as I know, being on the rebound isn't something positive - it means to be unhappy after a close, important relationship of yours ended, right? So why does it sound like a good thing in the example I quoted above? Is marrying someone on the rebound something good or bad? I'm a little bit confused here!