The Sega Master System is an 8-bit cartridge-based video game console that was manufactured by Sega and was first released in 1986 in North America (7 months after the original NES) and in 1987 in Europe. Its original Japanese incarnation was the Sega Mark III, which was first released in 1985.
When the system was later released in North America it was sold in two incarnations: a bare-bones console with one controller bundle called the "Sega Base System", and a bundle with two controllers and a light gun entitled the "Sega Master System". It was this latter configuration that became the more popular and better known of the two, and the system almost immediately became synonymous with this bundle. The system itself appears to have originally been intended to have been referred to as the "Sega Power Base" in English-speaking markets, and the Sega Genesis/Mega Drive adapter that lets you play Master System games was later referred to as "Power Base Converter".
In the European, Oceania and Brazilian markets, this console launched Sega onto a competitive level comparable to Nintendo, due to its wider availability, but failed to put a dent in the North American and Japanese markets.
The Master System was released as a direct competitor to the Nintendo Entertainment System in the third videogame generation. Despite its shaky performance in the major territories, it enjoyed over a decade of life in smaller markets.
The later Sega Game Gear is effectively a hand-held Master System, with a few enhancements, although it required an adapter to play actual Master System cartridges.
Source: Wikipedia, "Sega Master System", available under the CC-BY-SA License.