How would you exlain "router" functionality to non-technical people??
Basically, routing is the following:
It's like the sorting centre in a post office. Data from a network packet are like the letters you send, it contains information for the recipient. It reads the recipient's address (but instead of a post address, computers use MAC and IP addresses) from the internet packets (like mail recipients) and sends them off to the computer it is meant for (mail recipient). A switch very much works the same way, only a router is the only one of the two that keeps track of who are in the neighbourhood (network).
Nowadays routers have much more functionality, like wireless signal conversion (WiFi), modem functions, etc. But the above would be the basic routing function.
All good answers, but the OP was asking how to explain to non-technical people. In which case, I usually use a cable splitter analogy, because most people are familiar with that technology:
Cable TV comes into your home at one location, but you have two TVs in different rooms. So, you attach a splitter, which allows you to connect cables from the splitter to your two (or more) separate TV sets. A router does something similar, as your internet comes in via a cable connected to a modem. The modem has one ethernet output, which connects to the router. The router provides more outputs to connect to multiple computers, as well as wireless access.
I know it's not a perfect analogy, but when I start mentioning data packets and such, lay people get that glossy-eyed look and start wondering how long it will be until dinner, or at least until I'm done talking.
A router is a device in computer networking that forwards data packets to their destinations, based on their addresses. The work a router does it called routing, which is somewhat like switching, but a router is different from a switch. The latter is simply a device to connect machines to form a LAN.
How a Router Works
When data packets are transmitted over a network (say the Internet), they move through many routers (because they pass through many networks) in their journey from the source machine to the destination machine. Routers work with IP packets, meaning that it works at the level of the IP protocol. Each router keeps information about its neighbors (other routers in the same or other networks). This information includes the IP address and the cost, which is in terms of time, delay and other network considerations. This information is kept in a routing table, found in all routers.
When a packet of data arrives at a router, its header information is scrutinized by the router. Based on the destination and source IP addresses of the packet, the router decides which neighbor it will forward it to. It chooses the route with the least cost, and forwards the packet to the first router on that route.