A bird of prey is a predatory bird - how surprising - with very sharp eyes, powerful claws and a powerful hooked bill. Most of them fit one of the two main types:

flying forts
large birds with large, broad, slow moving wings that circle high above open terrain looking for something edible below, and drop down like stones to catch it (or, in the case of vultures, to be ahead of the competition)
fighters (chasers)
smaller, agile birds with narrow, pointy wings that operate in woodland and actively chase their prey in flight

A notable exception is the kestrel: a fighter by build that pretends to be a flying fort. It flaps its wings like mad in order to stay up in the air, which looks rather silly, but who can blame them - there's no arguing with success.

Taxonomically, the birds of prey come in three kinds: