What's Detachment Anyway?

So many of the saints have talked about detachment from things, from people etc. But I haven't quite gotten it. I just love people too much. I can't help myself. I am an emotional person, plus I am a huge extravert. I literally feed off of other people's energy. God made me this way so why would He then expect me to detach myself from them. People that is.
But we are also reminded that our God is a jealous God. He wants us for Himself. We can love the Creator but not become attached to those He created. I am so confused. Maybe I should look stuff up about this. Anyone out there have any suggestions? We are supposed to love people but be able to let go at a moment's notice. I just don't know if I am capable of that. It makes me tired even thinking about it.