How can we see light from galaxies 12+ billions of years ago?

First, the galaxy emitting the light doesn't just emit a flash of light and then stop, it is a constant emission of light. What does this mean? It means that there is certainly light emitted from that galaxy that has ped us by. But, the light we see now was emitted from the galaxy 12+ billion years ago. Light that ped us by from that galaxy yesterday was emitted 12+ billion years ago plus a day. Hope that makes sense to you.