Insecurity is a major problem in relationships. Indeed, a large number of other relationship problems ultimately stem from insecurity. If one or both of the people in the relationship do not have enough self-confidence to believe that they deserve the other person, they may try to build this self-confidence in unhealthy ways, such as bringing the other person down by insulting them, being jealous or even cheating on them. So, you should be on the lookout for signs of insecurity to nip it in the bud and build a healthy relationship.
If you are in a relationship with someone, it is likely they may criticise you from time to time, and vice versa. While overt criticism isn't healthy, since it immediately puts the other person on the defensive, a sign of insecurity is an inability to take even minor criticism. If you or your partner fly into a rage at the slightest admonishment, you should think about why the reaction was so strong. A secure person can take criticism and adjusts his behaviour without taking it personally; an insecure person, on the other hand, cannot.
Imagination vs. Reality
Secure people see things as they are. If your girlfriend says she's working late, the odds are that she is working late. Insecure people are not this rational. If you tell an insecure partner that you are working late and he refuses to believe you, it is because his insecure imagination is taking control of his perception of reality, unless you have lied to the person in the past and he has reason not to believe you. So, if you find yourself constantly explaining your behaviour and otherwise "proving" yourself, it's because you are in an insecure relationship.
Insecure people cannot believe that their partners have chosen to date them. So, whenever they see their partners talk to someone else, their imagination gets control of them again and they assume that their partners are interested in the other person. Of course, as with all things in relationships, this has degrees; some jealousy is reasonable, while other jealousy is not. If you find yourself having to explain exactly what your relationship is with everyone you talk to, though, you are probably in an insecure relationship.
Relationships are connections between two people. This means that you will naturally spend a lot of time with and around one each other. However, there's a difference between spending a lot of time with someone and being completely dependent on them for all of your social, financial and emotional needs. Dependency can be created by one or both insecure people; sometimes an insecure person tries to make herself dependent while other times an insecure person will try to make the other person dependent. Either way, if either of you is dependent on the relationship for every part of your happiness, then you are probably insecure.