A router essentially determines which way is the shortest or fastest in a network, and routes packets accordingly. It works at layer 3 of the OSI model, moving packets from one port to another based on L3 addresses - ie. IP addresses, IPX addresses, etc. A bridge connects one point to another in a network permanently. It works at layer 1 and 2 of the OSI model.
Read more: What is the difference between bridge and router