Here’s what my take on what Kara Thrace was:
If not specifically an angel, then she was obviously some sort of spiritual form with a very clear purpose: make sure all necessary circumstances align to break the cycle of “this has happened before, and this will happen again”. Whether or not she succeeded, I believe, is a question the writers suggest we, as the current occupants of the 14th colony, will have to answer.
How did she do this? Well, I imagine you, like me, throughout the entire series were asking yourself what does all this mean and how is it all coming together? The answer is Kara. She was never a corporeal person from the beginning–she was always a mystical being, whose own destiny even she was unaware of. But she was always in just the right place at the right time to make something important happen–she had prescient perception in her drawing of the mysterious symbol, as a child, she had performed the notes that corresponded to the coordinates where the new earth was located, she recovered the arrow of Apollo, etc. And why is it she wasn’t afraid of death and was such an ace pilot? Because she was immortal, even though she only realized this on a subconscious level. She had already died 5000 years ago. It’s why, for example, only she could kill scar when everyone else failed (even if she had help). And when her plane exploded, she simply rematerialized at a later time, never having been able to die in the first place, to finish her task. If it weren’t for Kara, all the circumstances necessary for Galactica and the fleet to survive and find Earth would never have happened. She was the X-factor that brought everything together. And she only became consiously aware of her subtle influence on everything when she and the phantom piano player discovered the enigmatic song which was the supernatural thread running through it all.
In short, if any of the other characters were in the right place at the right time to miraculously save humanity, it was because of something either subtle or significant that Kara had affected. So in the end, she realized she had done all she could and could finally rest in peace, as she had not done since she originally died in battle all those thousands of years ago. Ghost or Angel, it was her job to set things right.