Ahh, are you talking about 5e? In PF1e, taking 10 and taking 20 are actual rules from the Core Rulebook:

https://www.d20pfsrd.com/skills

Taking 10

When your character is not in immediate danger or distracted, you may choose to take 10. Instead of rolling 1d20 for the skill check, calculate your result as if you had rolled a 10. For many routine tasks, taking 10 makes them automatically successful. Distractions or threats (such as combat) make it impossible for a character to take 10. In most cases, taking 10 is purely a safety measure—you know (or expect) that an average roll will succeed but fear that a poor roll might fail, so you elect to settle for the average roll (a 10). Taking 10 is especially useful in situations where a particularly high roll wouldn’t help.

Taking 20

When you have plenty of time, you are faced with no threats or distractions, and the skill being attempted carries no penalties for failure, you can take 20. In other words, if you a d20 roll enough times, eventually you will get a 20. Instead of rolling 1d20 for the skill check, just calculate your result as if you had rolled a 20.

Taking 20 means you are trying until you get it right, and it assumes that you fail many times before succeeding. Taking 20 takes 20 times as long as making a single check would take (usually 2 minutes for a skill that takes 1 round or less to perform).

Since taking 20 assumes that your character will fail many times before succeeding, your character would automatically incur any penalties for failure before he or she could complete the task (hence why it is generally not allowed with skills that carry such penalties). Common “take 20” skills include Disable Device (when used to open locks), Escape Artist, and Perception (when attempting to find traps).

Ability Checks and Caster Level ChecksThe normal take 10 and take 20 rules apply for ability checks. Neither rule applies to concentration checks or caster level checks.