Most modern cameras have the ability to do constant autofocus in video mode, to varying degrees of quality and success. Usually they will try to follow anything that looks like a human face, or at least the brightest object in the field of view.

That said, even the greatest autofocus isn't going to be able to keep up with a person who moves around a lot at f/1.8 - so it's reasonable to stop down a bit if that's the case for your subject.