Have you seen people break up with someone then a couple days later they are with someone else they just met? This could be called a rebound relationship which is for the most part not a good idea. It's not good for the one that just broke up or for the other new person.
A rebound relationship is basically one that somebody gets into to fill that void after having split with another person. They can not be by themselves for a length of time because maybe they lack self esteem or any other reasons. They may find that they are jumping from one relationship to another never being able to make a commitment.
What should you do if someone like this wants to get together with you? You would be wise to pass on it because you are going to get wrapped up in their problems. Although if you dated but did not take it serious, you may be ok. Just be in control of your own life.
Those that are prone to getting into a rebound relationship would be better off if they took a few months to get over their past relationship before starting a new one. This will give them a chance to get over the break up and avoid the possibility of starting a new failed one right away.
It would be important to break this cycle so you can get back on track and get into a good relationship without the baggage of the previous one hanging over you. Put all the other ones behind you and move on with your life.