Formal objection to a member of the court or the military judge being allowed to continue to sit on a court-martial. There are two types: for cause - based on a fact or circumstance (such as conflict of interest) which has the effect of disqualifying the person challenged; and peremptory - each side is allowed to challenge one member (but not the military judge) and is not required to give any reason at all.

Source: Judge Advocate General

Someones right to object to or fight something in a legal case.

Source: California Courts.