In various arcade shoot em up games (such as Gradius), when you beat the game, it allows you to start over at the beginning of the game after viewing the credits. You keep the score you had when you beat the game, but the enemies in the levels become harder and the game becomes more difficult. This is called a loop. The game starts on loop 1 and when you beat the game it goes to loop 2 with higher difficulty and when you beat it again you start over with an even higher difficuly setting at loop 3 and so on.
"The Loop" is the local name for Chicago's downtown area, so named because of the way the city's elevated trains (or el) loops around the area. Also used with directions, such as "North Loop," "South Loop," or "West Loop." There is, however, no "East Loop" because that would put you in Lake Michigan.