We live in a beauty-obsessed age and success sometimes appears to hinge solely on the presentation of an image that is acceptable to the press.

This quote is saying that our society puts a lot of emphasis on how people look and how they present themselves. It suggests that people often need to appear a certain way in order to be successful–to have the media and public accept them. We live in a world where it matters a lot what we look like and how we are perceived, so people must learn to manage their image and make sure it is something that people will accept.