'Badly' in this context means 'very much' in the sense of 'urgently'. eg He badly needs a haircut = His hair looks terrible, and he really needs to get it cut as soon as possible. Your sentence means 'I desperately want an ice cream'.

The word "badly" gives a sense of urgency so the person or people you're talking to will know that you really, really want to eat some ice cream. (.^_^.)/