OpenWrt is a type of linux that can run on a router. Once linux is installed on a router then a multitude of other linux applications can be installed on the router and run on it’s processor. This lets you turn a router into a cheap, low power computer capable of running a small network. These routers can often be purchased a a even lower price than the Raspberry Pi. It is also a great way to repurpose a unused piece of hardware.
Unlike the Raspberry Pi these routers were not designed to run as general purpose computers. This means that they usually have a slower processor and less RAM. They also often do not have the ability to access external storage. Together this limits the capacity of the server created with these devices.
Before purchasing or obtaining a router to install OpenWrt on consult the following chart of compatible routers: