Recently, I've had and observed many conversations involving people who are offended or incensed or upset or confused by the phrase “safe space”. Often people will dismiss others as oppressively p-c when they use that phrase. I think there's not really a good, accessible explanation of what I understand people mean when they say 'safe space'. So, here's my attempt at explaining what I understand a safe space to be.
A safe space is a situation or place or scene where you don't have to defend your feelings.
Your safe space may be very unsafe for others. This is ok. Not everyone can be comfortable at the same time. For example, /r/atheism or tumblr or 4chan or the neighborhood bar are safe spaces for different people. A man cave is an example of a safe space. We don't often think of it that way, because the phrase “safe spaces” feels new. It's a new name for a very old idea.
Everyone deserves a safe space. For some people, most of the world is a safe space. These people are often the most hostile to the idea of others carving out their own space. They may not understand what it is like to not have a safe space.
Having to constantly assert the validity of one's feelings is tiring. If society makes you do this, if people constantly try to debate your feelings, you are being marginalized. (There are other ways to be marginalized, they are not less valid.) People who are marginalized often benefit from forming their own safe spaces. They aren't trying to make anyone else feel bad, they're just carving out a space where they can be comfortable.