Natural 1
When a d20 roll produces a one, that one is said to be "natural" (i.e. It occurred naturally and hasn't been modified by any bonuses). This is as poor a result as you can get, and in some cases it gives special results, depending on the nature of the check.
Attack Rolls
A natural 1 is always a miss. In addition, you risk fumbling. There is usually a 50% chance that something unfortunate will happen, at your GM's discretion. You may drop or damage your weapon, trip and fall Prone, accidentally hit yourself or a nearby ally and so on. It all depends on the circumstances and the GM's imagination.
Certain other conditions may apply as well. For example, if you are wielding a poisoned weapon and you get a natural 1 on an attack roll, you always have a 50% chance of accidentally poisoning yourself.
Skill and Ability Checks
A natural 1 qualifies only as a roll of 1. If you happen to be good enough to succeed even with a roll of 1, you still succeed.
Despite this fact, a roll of one will usually mis the DC by such lengths that the GM may choose to add extra dramatic consequences to emphasize the exceptional failure of this attempt.
Saves
A natural 1 represents automatic failure on a save.
In addition, the GM may rule, when appropriate, that additional negative effects are taken. The most common is the possibility of putting your equipment at risk when failing a save to avoid certain forms of damage.