It often means there is a (lack of trust). It's not uncommon for a person to wonder if their mate loves them as much they love their mate. Usually time and reassurance from one's partner removes that type of insecurity. If the person has been betrayed in the past they may always be looking for "signs" that it's happening again. No one wants to be a fool.
Extreme possessiveness on the other hand has nothing to do with insecurity but a lot do with "ownership". This type of individual does not want their mate to even spend time with family members. They don't want to see them being kind to others or even wearing a smile unless it has something to do with them.
Lastly there are those who believe being jealous is "proof of love". They view being (trusted too much) by their mate as a sign that he/she "doesn't care". Most people want their partners to mirror their behavior. If you're with a jealous person they expect you to be jealous at times. If you're with a trusting person they expect you to be trusting. Ultimately we're all looking for someone who agrees with us and most importantly "gets us". Opposites may attract in the short run but like attracts like in the long run.