It is a unique address given to a network adapter such as built in network cards on a motherboard when it is being made. It doesn't really do anything, it's just a unique hexadecimal value given to all devies that connect to a network. Not sure how it would relate to streaming.
As stated above, it's a unique ID given to each network card, kinda like IP addresses for Internet devices. It's how Ethernet tells different network devices apart. Let's say you're transferring a file on your LAN from a PC named Desktop to a PC named Laptop.
■Windows resolves Desktop to an IP address (say 192.168.1.100), and Laptop to an IP address (say 192.168.1.101).
■Windows takes a part of the file you're transferring, and encapsulates it in an IP packet (kinda like putting the data in an envelope) marked 192.168.1.100 as the sender, and 192.168.1.101 as the recipient.
■This IP packet is sent to the network card. The network card looks at the recipient IP address, and asks your LAN's DHCP server what MAC address that corresponds to. The server gives it the MAC address of Laptop's network card.
■The desktop network card then encapsulates the IP packet in an ethernet packet (again like putting the IP packet in an envelope) marked with the Desktop's MAC address as the sender, the Laptop's MAC address as the recipient.
■This ethernet packet is sent over the network cable to the switch the Desktop is plugged into. The switch says "I dunno who this recipient MAC address belongs to" and forwards the packet to the router.
■The router gets the ethernet packet, reads the recipient MAC address, compares it to the list of devices it knows are connected to the network, and finds the MAC address on the list of WiFi devices. It forwards the packet to the WiFi portion of the router.
■The router's WiFi module encapsulates the Ethernet packet yet again with lots of error correction coding to prep it for broadcast over WiFi, then transmits it.
■The Laptop's WiFi card sees the WiFi transmission, and that it is marked for it. It unpacks the WiFi packet, reads the recipient MAC address on the ethernet packet and confirms that it matches its MAC address. It unpacks the ethernet packet, and sends the IP packet inside to the Laptop's OS.
■The Laptop's OS reads the IP packet, confirms the IP address is intended for it, and unpacks the packet to get the file data contained inside. (There are more layers than this which I'm omitting for brevity.)
The only way I can see a MAC address affecting streaming is if your sysadmin (e.g. one of your parents) has put a block on your computer's MAC address for certain times of the day, so you can't use the Internet during those times. In that case, the above chain of events would fail when the router receives an ethernet packet with your computer's MAC address, with the Internet (WAN) designated as the recipient. The router would see that that MAC address is prohibited from accessing the Internet at that time, and dispose of the packet.