A "roving eye" describes a person's desire to look at someone other than his or her significant other. The term refers to the physical act of looking at someone else, that you find attractive, while you should be looking at your partner.
The term "roving eye" generally describes a male action. It is a social construct that men are unable to keep their eyes off of other women, even when they are in a relationship. Anyone, male or female, can have a roving eye.
Depending on how intense your relationship is will determine how much a roving eye matters. In general, a roving eye means very little unless your partner actually acts upon the desire for another person. If it does bother you, bring it up with him or her.
A man and his wife are sitting at a table together. An attractive woman passes the table, and instead of looking at his wife he watches the attractive woman passing by. We would say he has a "roving eye."