When using the weapon you selected, your threat range is doubled. For example, a longsword usually threatens a critical hit on a roll of 19-20 (two numbers). If a character using a longsword has Improved Critical (longsword), the threat range becomes 17-20 (four numbers).
You can gain Improved Critical multiple times. The effects do not stack. Each time you take the feat, it applies to a new type of weapon. This effect doesn't stack with any other effect that expands the threat range of a weapon (such as the keen edge spell).