Sorry to hear about your broken tooth. There are a few things that will probably happen over time, depending on the nature of break. One, the tooth may get a cavity or infection. If it is a small break this is unlikely to happen; at least not for a little while. However, if it is a large break it can happen rather soon. When a tooth breaks it usually loses its enamel covering. The layers under the enamel are porous and allow bacteria to get inside a lot easier.
This could mean that instead of fixing your tooth with a simple filling, it requires a root canal and crown, or even the loss of the tooth and an implant (the treatment gets more involved and much more expensive). Second, the tooth opposing the broken one will start to enter the space of the broken one. This will not be a problem and go unnoticed until you try to restore the broken one. At this point you would have to have work on both the opposing tooth and the broken tooth to make everything fit. Hope this helps.
My best to you!
William F. Scott IV, DMD