Coverage is the number of camera shots and angles that you have in a particular scene. When filming a scene for a film or television show, it is important to get as much coverage as possible. The more coverage you have, the more impressive the scene will look after editing. If the editor has a much wider range of angles and shots to work with then the more work he/she can do with them. This is especially important when shooting something you can only do once. For example, a very large explosion. A lack of coverage would mean that you may not get enough angles to fully portray the event, and the angles themselves may not be very good. It is always easier to pick out the best ones after the scene has been shot, rather than before.
Cutaways are when a continuous scene is taking place, and is interrupted by the camera cutting away from the main scene to flash to someone (or something) else. The camera generally flashes to someone who is being affected by what is goin on in the continuous shot. It is to show how they are reacting to the continuous scene. Although seemingly not entirely necessary when used most of the time, they allow for the editor and director to make a longer sequence of footage. When necessary they are most commenly used to inform the audience that the character in the cutaway has seen something that is important to the story. For example, if two characters kiss, and the partner of one of those characters observes this. It would show that character watching. This is so the audience knows what is going on. Cutaways are generally followed by a return to the initial shot.