The terminology generally refers to variants of the Ethernet over twisted pair technology that use a female 8P8C port connection on a computer, or other network device.
The X refers to the fact that transmit wires on an MDI device must be connected to receive wires on an MDI-X device. Straight through cables connect pins 1 and 2 (transmit) on an MDI device to pins 1 and 2 (receive) on an MDI-X device.
Similarly, pins 3 and 6 are receive pins on an MDI device and transmit pins on an MDI-X device. The general convention is for network hubs, bridges and switches to use the MDI-X configuration, while all other nodes such as personal computers, workstations, servers and routers use an MDI interface. Some routers and other devices had an uplink/normal switch to go back and forth between MDI and MDI-X on a specific port.
The requirement of connecting the transmitter of one side to the receiver on the other side and vice versa makes it necessary to always have an odd number of crossovers between two devices, with an MDI-X port containing an internal crossover.
Thus, connecting MDI to MDI-X requires a straight-through cable (one crossover in total). Connecting MDI to MDI (no crossover) or MDI-X to MDI-X (two crossovers) requires a(nother) crossover in the cable to get an odd number.
When using more complicated setups through multiple patch panels in structured cabling, the connection can use multiple patch and building cable segments. It is a good idea to have all necessary crossovers on one side, i.e. either on the central hub/switch or on each secondary hub/switch.