A check is the process by which the game decides whether a character suceeds or fails at an attempted action for which there is a chance of failure. Checks are used when players use active skills, use weapon attacks, make a save, or attempt to stabilize while incapacitated and bleeding.
The vast majority of checks take the form of d20 + modifier ≥ DC. If the expression evaluates to true, the check is said to be passed, and the character suceeds at whatever they were doing. For skill checks, the modifier is that character's skill modifier for that skill. For weapon attacks, the modifier is that character's attack bonus. For saves, the modifier is the character's save modifier.
Stabilization checks take the form of d100 ≤ 10. In the same manner as other checks, if this expression evaluated to true, then the character passes the check and is stabilized.