Routers are more like computers since they do a number of computations inside them, even though they are smaller in size. Routers tend to have many of the basic components that larger computers do. These components include a processors, an operating system, and memory. This means that on rebooting, they will be benefited from the fresh start.
Usually, the IP address of the laptop and the phone changes without any specific reason (in the terms of a layman). The router on the other hand does not recognize when this change occurs. So in order to sync the network connection, rebooting the router helps.