A MAC-address is the unique hardware address on a networks device. Every computer that has a networks adapter, a bluetooth card or similar network device has a MAC address.
If your computer has several network devices (for example most laptops have a wireless network device and a cable network device) you also have several MAC addresses.
These MAC-addresses are supposed to be unique. Every manufacturer has a range of numbers and they code it into every network device. Some of the manufacturers use numbers twice, but you get tech problems, when you have two computers with the same mac address on the same network segment.
So theoretically, if the numbers are tracked and the resale people keep you address they could find out which MAC-Address went to which person. But IT-specialists can also recode the mac-address on their PCs network device.
Originally the standard was a little unclear if each network adapter would have a unique MAC address or each server. Sun famously (infamously) chose the later. On older Sun servers each system would have a MAC address and every network port on it would use it. The assumption was that if you had a server with multiple network cards that they would be connected to different networks which was a pretty safe assumption in the days of routed networks but with switched networks it wasn't.. There was a way of giving separate ports different hardware addresses by settings in the non-volatile RAM but the process was different for every model of server. Now that Sun servers are largely based on Intel architecture components the NICs they purchase already have MAC addresses.