In law, recusal is the act of a judge being disqualified (or disqualifying herself) because of a conflict of interest. A recusal, for example, would replace a judge if the defendant in a case was a relative.
An attorney might ask for recusal if she overhears the judge saying something like, "Well it's obvious he's guilty — just look at those clothes he's wearing!" Before a case is decided, both judge and jury have to be completely unbiased and impartial for the result to be just. Recusal protects against a judge's bias. The word comes from recuse, "reject or challenge as disqualified to act."