I’ve decided to break it off with her.

"Break it off" is an idiom that means to end the relationship.

'It' is often used an an empty subject or object. It is raining. It is late.

Well,it s an idiom and all we have to do is to take it as it is. However,if you asked me, I would say that that 'it' refers to relationship. In other words: it=relationship.(in your context) I hope this will help you