Factory built wheels, are wheels which are supplied to the shop from the maufacturer, ie Mavic, Shimano or Campagnolo etc, as a complete wheel.
Each manufacturer supplies wheels to cover a range of uses, eg. time trial, track, ATB and usually a range of general purpose road wheels of varying qualities and weights.
Time trial wheels generally have deeper rims, the better ones being carbon to keep the weight as low as possible. Less spokes can be used not only lower the weight of the wheel but more importantly improve the aerodynamics.
The lighter and better quality time trial wheels are usually designed for tubular tyre use, which makes it possible for the rim weight to be reduced and the strength of the rim to be increased.
Track wheels are pretty specific in that they have a narrower rear hub than road wheels as there is only one fixed sprocket to accomodate, rims are usually tubular (or sprint rims as they are sometimes called) as there is little risk of puncturing on the track but a well glued on tubular tyre should be controllable should a puncture occur. Most factory built track wheels tend to have deep rims, usually carbon fibre mainly for aerodynamic reasons, there are some deep aluminium rimmed track wheels but, being heavier, tend to take more effort to accelerate resulting in a slightly more sluggish feel.
Road wheels cover quite a range of weights and qualities and as a result a pretty wide range of prices also. Aluminium rims tend to be more common on road wheels, as shallower rims have less of a difference in weight and aluminium rims are cheaper to replace if they get damaged.