Sequence breaking typically entails the use of unintended glitches, or unintended mechanics of one's items or environment in order to reach different sections or equipment out of order. Usually, these techniques are difficult to master and require large amounts of trial and error; thus most instances of sequence breaking are left to extremely dedicated players to discover and exploit. Sometimes this is done in tandem with speed runs or minimalist runs.
Shadow Complex, a 2009 game that is somewhat of a homage to games like Super Metroid and Castlevania: Symphony of the Night, also contains sequence breaking, but Chair Entertainment put these quirks in the game intentionally. Therefore, it could be argued that this is not really sequence breaking, but because Chair have refused to reveal how to sequence break in the game, players must still discover the techniques the old-fashioned way.
Super Paper Mario referenced the term while breaking the fourth wall; at one point, an NPC complains that the player is "a sequence breaker" after beating him.