Offrace means that a player has selected a different race than their usual, preferred, "main" race.
If a player wanted to play a different race in a professional game during the KeSPA era, he or she had to announce it one week before the match. This rule gave the opponent the opportunity to prepare for the new situation.
Nowadays almost no player offraces in a serious match. In the early days of Broodwar it was common that a player was capable of playing two or even all three races, but today the level of play is so advanced that it is almost impossible to be able to play all nine matchups at an equally high level. There is the notable practice of racepicking, often to avoid mirror match-ups; at the moment there are no Korean Progamers who do that in competitive play.
A good opportunity to watch Progamers playing their offrace can be found through recorded Korean TV shows like B.net Attack or I love Star. In one of the most famous episodes of B.net Attack, Bisu played a PvT against sAviOr on Blue Storm.