Personal injury law protects your right to control what does or does not touch your body. An assault is an act, or threat to act, that is intended to put a person in fear of imminent non-consensual physical touching. The tort of assault protects people from the fear that they will be physically harmed. Actual physical contact is not required, and in fact, if there is physical contact, the assault becomes a battery.
Note that this is different than what many people are familiar with in the context of criminal law, where assault and battery are terms that are defined by specific criminal legislation, which defines the criminal penalties imposed for engaging in certain acts, rather than the right to monetary recovery which is governed by personal injury law.
Example: If you intentionally throw a rock at someone, and the person sees the rock being hurled toward him and is in fear of being hit, you would be liable for the tort of assault. If the rock actually hits him, the assault becomes a battery. In this example, obviously the tort of battery has greater potential liability than the tort of assault. Note that if you did not see the person and threw the rock where he was standing, there would be no assault since there would be no intent on your part. In that event, if the rock hits the person you could be liable for negligence, but not battery.