An opposed check occurs when the success of an attack (spell, feat or otherwise) is determined by the target's skills, abilities or other attributes. This is different than a check against a set DC (as with disabling preset traps) or avoiding harmful effects (as with a saving throw).
An example of an opposed check is the Discipline check when attempting a Knockdown: if the attacker hits, the attack roll (attack bonus + d20 + size bonus) is opposed by the target's Discipline check (Discipline + d20), and the attacker must beat it (equal or surpass it) to succeed in knocking the target down.