Every network port on your computer has a MAC address, a unique 48 bit identifier. It's a bit like an IP address but lower level; your wireless or ethernet delivers Internet packets to you by knowing your MAC address.
It's very important that every computer on a network has a unique MAC address. So important, that all network hardware has a unique ID burned into its firmware (one of only two sources of standard unique bits on a typical PC). However, it's common for routers to support "MAC address cloning", where your router impersonates your computer when talking to your ISP. That feature was placed there to work around inflexible ISP networks and network policies, and it's mostly useful.
But MAC address cloning can be quite harmful, as I learned today. See, I cloned my laptop's MAC address to my router. Then two years ltaer I cloned my laptop's MAC address to my new router, too, in my new house three miles away. Miraculously this worked fine for a year, until this morning. When my network connection would go down at random intervals. I'm guessing the layer 2 stuff wasn't broken by the duplicate MAC address but rather it confused some DHCP housekeeping in my ISP's network management back office.
Three cheers to my wonderful ISP, sonic.net, for helping me figure out this bizarre problem. I love that when I call them I get a tech who will happily discuss DHCP leases, MAC addresses, and non-standard router firmware wtih me. They were as mystified as I was at first, but talking it over at the phone we figured out something was going bad with address assignment. No way either of us could have figured this out without working together.