Complex sentence: A bench warrant is a variant of an arrest warrant which authorizes the immediate arrest on sight of the individual in question who is in contempt of court possibly for failing to appear at the appointed time and date for a scheduled court appearance.
Split into simpler sentences: A bench warrant is a variant of an arrest warrant, which authorizes the immediate on-sight arrest of the individual subject to the bench warrant. Typically, a bench warrant is issued for a person in contempt of court--possibly as a result of that person's failure to appear at the appointed time and date for a mandated court appearance.