Atoms are most stable when they have a certain number of electrons around them, described as "having a full shell". A neutral chlorine atom is one electron short of having a full shell, and a neutral sodium atom has one electron more than a full shell. Therefore, neutral chlorine will rip an electron off just about anything, causing damage, while neutral sodium will push its extra electron away, same deal. That is why they are such reactive chemicals. Once they've done that process they are stable.

Then, as the other poster described, they are oppositely charged, so they are attracted to each other with medium strength, but not strongly bonded, which, to simplify it somewhat, is when atoms share electrons which both of them would like to have.