Selective-fire, or "select fire", is a property of some firearms which allows the user to change their mode of firing, usually by means of a switch. Typically, this allows it to alternate between semi-automatic and automatic firing, or occasionally it incorporates a burst-fire mode.
The example you are most likely to be familiar with is the Glock 18 Select Fire, the terrorists' starting pistol from the game Counterstrike. This handgun can alternate between semi-automatic (where pulling the trigger fires one round and loads the next one into the chamber) and burst-fire mode (where several bullets are fired in quick succession). The selective-fire switch acts as a safety, preventing you from using excessive force as well as conserving your ammunition.
Some select-fire weapons, usually military weapons, allow the wielder to choose between semi-automatic and automatic firing by means of a special select-fire trigger rather than a seperate switch. Such a trigger can be pulled with either a lighter, or a harder strength, firing semi-automatic mode if the trigger is pulled "easy", but fully-automatic mode if the trigger is pulled hard. This is not only quicker than a switch, it's also more intuitive, as pulling the trigger with greater strength discharges bullets more quickly, as opposed to holding anything back. The FAMAS assault rifle from Metal Gear Solid is operated somewhat like this, firing a single shot if the button is tapped once but firing in automatic mode if held down firmly.
Select-fire weapons are currently classified in the USA under BATF Class III, since they are essentially machine guns. (A select-fire uzi falls under this category.) Obtaining a license for one requires that you are at least 21 years of age and have no prior felonies, violent misdemeanours - in other words, your right to keep and bear arms1 really does let you own an uzi, as long as they can be reasonably sure they can trust you with one. See karfung's writeup for further information.
1As part of a well-organised militia, being necessary to the security of a free State.