Honestly, I don't want to view her as a person with depression but I don't want to ignore her either. Please give me a rough overview of depression (I couldn't understand a word wikipedia said other than 'sad' 'depression' 'sometimes suicidal') and how to encourage her to come back for choir.
I don't really have any advice for you how to deal with it, because it's not something that you can really deal with or get her out of it. Depression is a very deep wound in someone's psyche, and it requires a lot of work to overcome. Encouragement doesn't really affect it that much, and if you did manage to convince her, she'd probably be very reluctant in it anyway.
Given your social anxiety, this should be easy for you to picture if it's described in the right way, and I'll try my best to do that.
I think the best way to try to understand depression is to try to think to the saddest moment in your life. Combine that with a feeling of unease and uncertainty. Add the tension placed on you to live a happy life and whatever other expectations that are placed on you. Add in whatever other mental issues you have and whatever stress you have in your everyday life that you feel. Your hope is drained and mostly nonexistent. You have an empty feeling, like you're missing something important. You don't enjoy the things that you used to enjoy. You become anxious. You become disinterested in the world and the important things in life, like friends and family.
You have an anchor attached to your heart, and its sinking into your chest.
Now imagine, you come home from a night out with friends. You had a good time with them. It was really enjoyable. You went to a movie, had a few laughs, and went out to eat before calling it a night and going back home. When you get home, there's someone there waiting for you. It's the embodiment of all of those feelings. This person is someone you're familiar with. He's been a "friend" of yours for what seems like your whole life. He likes being around you, but you don't like being around him. Being around him makes you sad. Being around him gives you all of those feelings of hopelessness and dread that I described above.
Now imagine that friend being around you all the time, everywhere, sitting in the corner of the room. When you look at him, those feelings come to you. You try not to look at him, but something draws you toward him when you aren't distracted by something else. And when you are distracted by something else, the urge to look is still present in your mind. You try to fight it, but it becomes overwhelming, and you eventually look.
It's kind of like that. A persistent, overwhelming negative aura that consumes your innermost thoughts. It makes you second guess everything. It makes you look at yourself poorly. It affects your self-esteem, and lowers your self-worth. You start to feel like a burden to those around you, because you don't see any value in yourself, so how could anyone else see any value in you?