A dome works as a type of enclosure, keeping people away from the environment. But usually the way that they work is to keep the environment within and to let people to view that occasionally. This same definition or way of viewing the dome also carries over into the idea of sports domes too whether you like it or not.
If you have a dream about a dome then this means that you are close to a major goal that you have. Domed buildings usually represent sites of importance in the real world. If you have a dream in which you see a domed building it means that you are getting closer to reaching a major goal that you need to meet right now. The dome on the building represents the place that you need to reach at all costs. This is where you need to get to or else you will start to fall back and renege on your true dreams in life and all of the expectations that you held for yourself.
A dome also represents an enclosure. If you have a dream about a dome it could be because there is some part of yourself, some aspect of your personality which you are guarding intensely and don't want to let anyone else in on. This is perfectly natural but also not necessarily all that healthy. If you want to grow up well and have good experiences in life you would do well to let your true self out once in a while.