A Seeker is a player in Quidditch who's seen as the most important player. There is only one Seeker per team.
The game ends when one of the teams' Seeker catches the Golden Snitch, which earns the team of the one who caught it an extra 150 points, so statistically, the team whose Seeker caught the Snitch nearly always wins. The only occasion in which a team whose Seeker didn't catch the Snitch could win would be if that team's Chasers scored more goals than the number of goals the other team's Chasers scored plus 150, which is extremely rare.
In ancient history, some people were playing an old-fashioned version of Quidditch, when a man named Barberus Bragge released a bird called a Golden Snidget into the arena and said that the person who caught it would win 150 Galleons. The game was ignored and only ended when a woman named Modesty Rabnott freed it. This started a tradition of throwing Snidgets into Quidditch games and adding an extra player (then called the Hunter) whose job was to catch it for 150 points, as a nod to the aforementioned 150 Galleons. However, because the Hunter's job also involved killing the birds, they became an endangered species and so the Snitch was introduced and the player got renamed the Seeker.