This question in its current state may be too broad, so I'll clarify.
Obviously, most routers today are a combination modem, WiFi transceiver and router, taking the signal off the phone line, converting it, and then sending it either over copper, F/O, or 802.11.
But what does the router actually do when it "routes"? From studying the TCP/IP stack, it's clear that source/destination addresses and ports occur in a few different points of the stack, so it at least seems like the endpoint devices should be able to do their own discrimination, simply ignoring packets not intended for them. To add to the confusion, this seems like the primary system 10BASE-2 relied upon, every device in the link being patched over the same connection.
So, what is the router doing with the data when it comes in (assuming the WiFi and modem stuff is taken out of consideration)?