The male gaze is the way in which men view who and what is presented on screen, often women. It is also how men view themselves due to how men are stereotypically represented in the media. The male gaze is often the dominant ideology, therefore a lot of women look at themselves and other women through a male gaze and judge how they look through a male perspective as they feel that they have to be visually pleasing to men. Women then become objectified.
Whether or not the female gaze actually exists is arguable as it simply reaffirms the male gaze of male power and dominance. The way most women see men is they way that men want to be seen themselves, eg: strong, muscular, powerful, wealthy, etc. Because of this, the question of the female gaze's existence is questionable as it is more of a male gaze but through a woman's perspective on a man.
I do agree with these theories in that they do exist and are quite prominent in todays society. Whilst these views can be quite objectifying and sexist (especially towards women) they are useful when creating things such as advertisements as they allow you to reach out to your target audience more. For example, by including a half naked or overly sexualised image of a woman in an advert directed at men, you are more likely to gain a male audience (the target audience) as it is what a man typically wants to see. This supports the male gaze as men see women the way they want to and woman see what they then feel is what men want them to be like, therefore they try to aspire to be like the women that are used in the adverts.
An example of the male gaze is depicted above. In this case, the breasts are the only part of the woman that are on show, simply to draw men towards the advert. This advert objectifies women as it shows them as sexual objects which are there 'for men'.