I'm not "them" anymore but I'll try to explain what I can.
Safe space used to be a term for a very small group of people who agreed to be positive and nurturing towards one another no matter what. This is important for sexual assault survivors, closet gays, the heavily marginalized, etc. to have a space in which they can actually speak with other human beings about their experiences. This is, in reality, a very important thing.
However, it doesn't scale well. Some people have thought, "Hey, I like these safe spaces...what if we make everywhere a safe space? Wouldn't that be great?" What they miss is there isn't one universal definition of safe space and you can't just force your definition upon others.
In a very general sense, at the reddit scale, "safe space" means protecting those who need protecting. That means protecting the disempowered, the marginalized, the minorities, etc. from the ignorance and violence of the masses. Protecting them from the hegemonic power of the majority, which means the patriarchy in general and if we're being honest white males in particular.
It sounds good in principle but who is "empowered" and who is "disempowered" isn't an easy question to answer. To make things worse the tools of enforcing a safe space are so powerful that the people fighting against oppression often become oppressors themselves. In the case of reddit there are many members who are openly abusive and believe it's morally justified because they're "punching up" and it's only real abuse when you hurt people lower on the social ladder than you. (As an aside, this a big reason to claim victimhood: once you're a "victim" you get to do things you otherwise wouldn't.)