tl;dr - A critical failure or success doesn't normally have any special effect, but a DM can choose to give it one.

DMG, page 242

CRITICAL SUCCESS OR FAILURE
Rolling a 20 or a 1 on an ability check or a saving throw doesn't normally have any special effect. However, you can choose to take such an exceptional roll into account when adjudicating the outcome. It's up to you to determine how this manifests in the game. An easy approach is to increase the impact of the success or failure. For example, rolling a 1 on a failed attempt to pick a lock might break the thieves' tools being used, and rolling a 20 on a successful Intelligence (Investigation) check might reveal an extra clue.

PHB, page 194

Rolling 1 or 20
Sometimes fate blesses or curses a combatant, causing the novice to hit and the veteran to miss. If the d20 roll for an attack is a 20, the attack hits regardless o f any modifiers or the target’s AC. In addition, the attack is a critical hit, as explained later in this chapter. If the d20 roll for an attack is a 1, the attack misses regardless of any modifiers or the target’s AC.

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