You are thinking of what is called a snake. It is a cable (pretty thick) with a number of individual XLR cables in it. One end has a box with all the XLR and TRS sockets, and the other with a fanout of the mating plugs at the other end. The mics and such plug into the box, the fanout to the mixer and other FOH* equipment. You can also get smaller ones that the box end goes on stage, and the fanout to the main snake, or mixer.
There are digital snakes, which link the stage and FOH with Ethernet, AES, or something proprietary, but use a much smaller cable in any case.
Last, a digital mixer, which you set up adjacent to the stage. What is at FOH is mostly just a remote control for the digital mixer, and that can be wireless.
*FOH stands for Front Of House, where you ordinarily have the mixer and processors and stuff, and the person operating the equipment.