I've been diagnosed with a high arched palate. what does this mean?

High arch palate: A high arched palate in isolation is not a problem. It can however occur as part of the physical manifestations of different syndromes that have other head and neck abnormalities and hearing loss.

Nothing in itself: High arched palate in the context of hypermobile joints can be a sign of marfan's syndrome, but that in itself may just be a normal variation. We humans come in all shapes and sizes :).