'Is it wrong to start dating right after a break-up?'

What exactly is a 'rebound relationship'? My friends have been warning me about the possibility of getting into one because I just broke up with someone a few weeks ago and have recently begun dating someone else.
People sometimes get into new relationships soon after the end of an earlier one because they are vulnerable and susceptible to anyone who comes across as kind and caring. They believe this will help them heal but, often enough, find that it only complicates their lives further. Maybe your friends just want you to take some time to get over your last relationship before you end up in another one. The grieving process takes time and maybe you should consider getting into a new relationship only when you're on a stronger footing, emotionally.

My friend and I have been considering the idea of having sex just because we can. We are not in a relationship, but we think we can deal with this. Are there things we need to consider before just doing it? We don't want the hassle of dealing with relationships because we have both been through bad break-ups before. This seems like a simpler solution.
This is tricky on a number of levels because of how it can affect the bond you currently share. I get that it's convenient and supposedly comes without the fuss that accompanies other relationships because you are both friends, but it's easy for feelings to develop and change with someone you share any sort of physical intimacy with. What if you do end up getting into a relationship, for instance? What happens if it doesn't work out? Or what happens if one of you gets into a relationship with someone else and is compelled to end this arrangement? Will the other person be okay with it then? Maybe you both need to discuss these possibilities too, before deciding to do anything. If your friendship is more important than anything else, that ought to be your priority.