A single-core processor is a microprocessor with a single core on its die. It performs the fetch-decode-execute cycle once per clock-cycle, as it only runs on one thread. A computer using a single core CPU is generally slower than a multi-core system.
Single core processors used to be widespread in desktop computers, but as applications demanded more processing power, the slower speed of single core systems became a detriment to performance. Windows supported single-core processor up until the release of Windows 11, where a dual-core processor is required. 
Single core processors are still in use in some niche circumstances. Some older legacy systems like those running antiquated operating systems (e.g. Windows 98) cannot gain any benefit from multi-core processors. Single core processors are also used in hobbyist computers like the Raspberry Pi and Single-board microcontrollers. The production of single-core desktop processors ended in 2013 with the Celeron G470. 
The first single core processor was the Intel 4004 which was commercially released on November 15, 1971 by Intel.  Since then many improvmements have been made to single core processors going from the 740kHz of the Intel 4004 to the 2GHz Celeron G470.