Moving pushes you out of your comfort zone. Of course this is going to come with disadvantages such as stress, but ultimately moving out of your comfort zone is the best way to discover and learn new things, about yourself and about things around you. If you have a family, moving is one of the best ways to teach children how to socialize and adapt to their environment, and I am personally grateful for that learning as a child.
2. You will meet new incredible people. Whether new neighboors, new colleagues, new gym instructor, moving is a great way to make new relationships and life-lasting friends. Of course the other side to this means leaving behind your friends from home, but I don't see it that way really. The people from home that matter most to you, you will always keep in touch with. In a way moving helps you figure out who you really want to keep in touch with, and those you will not lose.
3. Moving brings challenge and change, and good things come out of both. One of the great causes of unhappiness is boredom, and moving is a great technique against it! Challenge and change keep you motivated, at work and with everything else, and ultimately will contribute to making you happy.