zoom is short for zoom lens or zoom objective.

The distinctive property of a zoom lens is that the user can change its focal lenght. This is useful in filmography for certain effects, and in photography because of the convenience of carrying around only one lens instead of several fixed focal lenght lenses (also called primes).

You may ask, why don't they stop making primes then ?

There is in fact a dark side of the zoom.
Notice that this is A1 grade flamebait, photographers will bitch and moan and become positively irrational when the zoom-vs.-prime dispute starts. Actually, many photographers will become irrational over any technical point on which they happen to have an opinion.
Anyway, I fearlessly declare that a zoom lens, all other things being equal (I am not comparing a $50 dollar prime from the '50s to the $3000 80-200 zoom that Nikon will design next year, OK ?), when compared to primes

  1. Is heavier & bigger: a zoom lens has more glass inside, and glass is heavy.
  2. Is optically "worse": more glass (actually, more lens elements) mean more air-glass interfaces, which mean more flare, more parasite reflections ...
  3. Is less bright: in my opinion, the real killer. It is smashingly expensive to make a 35-80 mm zoom that opens up to f 2.8 - it is even more expensive to make an f1.8 one: so much, that nobody makes it.
  4. Is more complex mechanically
These limitations make zoom lenses inappropriate for many applications. Of course, the convenience factor makes them the lens of choice for others, like photojournalism.
Not to state the obvious, but a zoom lens (like almost everything in photography), is a tool to be applied to a problem in order to obtain certain results.
It is up to the photographer to determine whether it is the right tool.

Many zoom lenses (cheap ones chiefly) are varifocal. Most are variable aperture zooms, which means that as you zoom the aperture (the f stop) changes. This can make light metering complex, particularly if your camera suffers from a less-than-smart metering system.

Photo zooms usually are either a two-ring design, where one ring control focus and the other controls zooming, or a pump design, where pushing and pulling on the focus ring controls zooming.

Videocameras and compact cameras, particularly consumer ones, come equipped with zooms because of two reasons: first of all, the consumer wants to zoom and secondly, image quality is going to suck anyway.