To 'go off' something (or someone) means to lose interest in something (or someone). For example she used to drink coffee but read somewhere that it was bad for her health so she stopped drinking it. So.... 'she's completely gone off coffee lately.. because she thinks it's bad for her health.' The word 'completely' here means she has REALLY finished with coffee, she is not just giving it up for a day or two.

I've completely gone off salt and vinegar crisps lately. I used to love the things but now they make me feel sick. So I haven't quit eating them exactly. Wasn't a deliberate choice/decision. I just don't fancy them at the moment. Horses go off their feed. Pigs, I doubt, ever go off food! You can go off something a little bit, or completely, depending on how much you feel like avoiding it. Don't confuse it with "going off FOR a coffee" which IS going somewhere FOR a coffee.

It's British English, I think it's common in the UK, but it's never used by us Americans. I'm fairly sure it means that she's quit drinking coffee.