The guy on the left is the camera man, or shooter. That is a video camera that he's using; it's one of those awesome new cameras that captures HD footage but doesn't look much bigger than a still camera.
The guy on the right is the grip. When you have a big crew, a grip's job is to manage camera rigging and, depending where you are, sometimes lighting. When you have a small crew, a grip's job is a little bit of everything and anything to make the shooter's life easier. That usually involves helping to move equipment, having backup cards or tapes, and helping with set ups. Since the shooter is focused on what he sees in the viewfinder, the grip will also serve as an extra pair of eyes and ears when there's moving machinery.
The umbrella was a new one for me, though. We were afraid that it was going to rain, and expensive cameras and precipitation don't mix. But we only needed one more shot to finish up for the day, and no one wanted to give up just yet.
So out came the umbrella. We got the shot, no cameras were harmed, and got out of the field before the rain really started.
Problem-solving at its best!