A series of personal computers sold by Tandy Radio Shack. The '80' refers to the use of Zilog Z-80 processor (NOT Intel 80x8x).
There were 7.5 computers in the TRS-80 line: Models I, II, III, 4, 100, 102, 200. The Model 4P was a portable version of the Model 4 with no tape drive -- only 2 1/2-height single sided disk drives.
Later models that Radio Shack produced were not TRS-80 machines -- they were based on the Intel 80x8x architecture. These included Tandy 1000, Tandy 2000, Tandy 3000, and others. The 1000 had a proprietary Color card. The 2000 was a powerful machine for its time, but was based on the Intel 80186, so when IBM didn't build a computer based on this chip, it failed. It was used to design a boat for the America's Cup.
The TRS-80 GUI, DeskMate, was proprietary, but no more than Windoze at the time.
Many joke about "TRaSh-80" machines but several models were in fact classics of their time.