A router is a physical or virtual device that receives analysis and moves incoming packets to another network. It is also used to convert the packets to a different network interface and drop them. It finds the fastest way to reach the destination and then proceed accordingly. A router is also work as a gateway where two or more networks interact at every point of an internet presence.
If you have physical access to the router, you can usually find the model information on a sticker on the bottom or back of the router. Most of the time it will be clearly labeled "Model." If you do not have access to the router, or the sticker is damaged or missing, you can find the product model number on the router's online administration page.