Media or Medium reffers to the communications medium (cable, fiber, radio etc) over which communications happens.
Originally Ethernet used a "Shared medium". That is something (specifically a coaxial cable) where multiple devices can transmit but only one can successfully transmit at a time.
The medium access controllers primary job was to control access to the medium. It would receive a frame from the host computer, wait until the medium was free and attempt to serilaise and transmit the frame, performing backoff and retransmission if needed. It would also deserialise and usually filter incoming frames. Each medium access controller had a unique address known as a MAC address that could be used to identify the source and destination of frames..
With modern links running in full duplex mode there isn't any need for medium access control, the sender can just transmit immediately, but we still call the part of the network controller that handles serialisation, deserialisation and filtering a MAC and we still call it's address a MAC address.
Such is history, it's a bit like the way we still use a floppy disk as the save icon even though hardly anyone uses floppies anymore.