Sequence breaking is the act of completing a game in a different, unintended order, usually using a glitch or bug to bypass one or more obstacles placed there to prevent movement in that direction (at that time). One example is in Metroid Prime where you can use a small error in a level to reach an item very early in the game, instead of having to defeat several bosses and acquiring other items to be able to go there. The GBA game Metroid Zero Mission actually had deliberate sequence-breaking possibilities built in for the really hard-core Metroid fans.
Sequence breaking is commonly used in speed runs to complete the game as quickly as possible.