Essentially, anxiety and phobia have roots in trauma. Put simply, when a person experiences a trauma, even a "small" one, the brain records it. The next time the person experiences something similar to that original trauma, the person reacts in a way that is an effort to keep the person safe, even if the danger has passed.
An easy example: an 8 y.o. gets bit by a dog. For some people, that experience will make the person be afraid of dogs for the rest of his life. Not all dogs bite, but to that person, the danger is very real and persistent. If this fear gets too severe, even a picture of a dog will cause that person to have a fear reaction which can be paralyzing and debilitating. At this point, the simple trauma will have moved from anxiety about seeing a dog to a full blown phobia.
Hypnosis and guided imagery is incredibly effective in helping people who have anxiety and phobias. Essentially, hypnosis will help the person to separate his/her association with the trauma with the debilitating fear reaction that has evolved as a method of self-preservation. Simply stated: hypnosis can help the person to have a healthy fear response. The goal would not be to remove the fear, but rather to help the person react appropriately.
Consider this example: a 45 y.o. goes scuba diving and encounters a shark. The shark is simply swimming away. However, the person happened to see the movie "Jaws" when he was a kid and he was scared enough by the movie that he could not sleep well for several days after seeing the movie. Now, as a 45 y.o., he hadn't thought about that movie in years, but seeing the shark in that setting brought him right back to the point in time when he saw that movie and he felt the fear that came with it. After experiencing the shark, the person has reacted with such a strong self-preservation response that he won't even get on a boat.
In this example, we would not want to use hypnosis to remove the fear, but rather help the person to have a healthy fear and respect for sharks. Sometimes a healthy fear is desirable, since certainly sharks can be dangerous.