Typically used with Courage.
In short: be brave. When danger rears its ugly head(s), some fight, some take flight, and some pee their pants. Guts checks are called for when a creature or situation is particularly terrifying. Situations like encountering a towering monster which could swallow people whole, facing off single-handedly against an army, or overcoming the object of a character's phobia in order to move forward are terrifying.
Fear, or terror, is different from horror in that terror is usually acute and short-lived and once the object of the terror has passed, the character continues on as normal. The effects of something horrifying, on the other hand, affects a character's notions of reality and can be felt for days, years, or a lifetime. The Sanity Skill is used to deal with horrifying situations.
Guts checks are also used to oppose attempts to Intimidate or demoralize.
Guts checks are usually in response to the actions of another creature. However, there are times when you need to face your fears. When standing your ground, the higher the DL, the scarier the situation.
Guts checks are used versus Intimidate checks. They are also used against some Magic Spells and similar effects. In this case, Magic Defense can be added to the roll.
Guts attempts may be retried in some situations if the GM allows, and only when the fear is a continuing nuisance. Guts checks to resist Intimidation during combat cannot be retried without spending a fate point.