A continue in the Super Monkey Ball series is when you run out of lives and continue the game with another set of lives. However, this resets the score and bananas.
In Super Monkey Ball, you get six continues at the start of the game, but you can get more continues by getting 2500 play points after unlocking all mini games. You can get up to ten continues then after that you unlock infinite continues.
In Super Monkey Ball 2, you still get six continues but you can't get them. Instead, you can get lives with 500 play points for each life after six new party games unlocked. You can get up to 99 lives by getting 48,000 points.