The idea of “male gaze” flows from a psychoanalytical/philosophical theory brought into wider use by Jacques Lacan, but it is a huge subject and difficult to summarise.
According to this theory, and to put it at its most crude, the “gaze” is the relationship between the subject’s desire to look and the knowledge that one can also be viewed. The idea is that in our desire to look, we realise we can be looked upon. Then we lose some of our ability to govern our own behaviour; this process is tied into the idea of ego. We change our behaviour in accordance with who we wish to be.