A cat who is arching her back quite dramatically is doing so as a defensive reaction. When threatened she will do this to make herself look as intimidating as possible. In animals this is a very common reaction. For example, the cobra does this when it raises the front part of its body and spreads out its neck, and dogs will make themselves look as big as possible to send an intimidating message. Cats have flexible spines which contain twice as many vertebrae as humans which enables them to do this. When a cat performs this action it is typically accompanied by her fur standing on end. This is known as piloerection, which helps to enable her to look more larger and fearful than she actually is. This cat body language in translation is meant to send the message of “back off, don’t mess with me”, and although usually fear-based, cats will sometimes act out with aggression if they feel like they need to protect themselves from harm.