Natural roll

A "natural roll" means that when a die is rolled the result is the specific value of the die's face. This is without any additional modifiers for the specific purpose of the die roll.

Example
A d20 is used to see if a character succesfully hits an opponent. He adds his base attack bonus to his attack roll along with other modifiers (such as his strength modifier). If a 20 is the die's roll-value, this is a "natural 20" even if his base attack bonus etc modifies the final value to a different value.

Important values
The highest and lowest values of a die are often given additional significance compared to the intermediate values.

Auto-success
The highest value of a dice (e.g. 20 on a d20) is often used as "auto-success" for some checks, such as attack rolls and saving throws.

e.g.

Even if the final numerical value of an attack roll would mean an unsuccesful attack, the importance of the "natural 20" would mean that the attack would automatically succeed.

Auto-failure
The lowest value of a dice (e.g. 1 on a d20) is often used as "auto-failure" for some checks, such as saving throws.

e.g.

Even if the final numerical value of an saving throw would mean an succesful save, the importance of the "natural 1" would mean that the save would automatically fail.