Cyclists who participate in time trials seriously and often will want a time-trial-specific bike. Time trial (TT) bikes are designed for one thing only, and that is riding very, very fast over non-technical terrain. Time trials typically feature either flat or rolling courses - unlike road races, which often have steep hills, technical switchbacks and sharp corners. TT bikes are as aerodynamic as possible, putting the racer into a very low and powerful position - not the most comfortable for long distances, but extremely efficient.
One of the major differences between a road bike and a TT bike are the handlebars. TT handlebars have the shifters positioned on the forward end so that when the racer is in the aero position, no reaching or moving the hands is necessary - however, since time trials are solo events, there are no brakes on the end of the aero bars. Brake levers are positioned on the "bull horns", the wider part of the handlebar that the racer uses when cornering hard, or braking. This requires a more upright body position and wider hand position (similar to that of a road bike), which is far less aerodynamic than the TT tuck used in racing. This rather awkward brake position, and the narrow and somewhat precarious hand position makes TT bikes dangerous for road racing (in fact, they are banned from most sanctioned races).
The frame, seatpost and wheels are also designed for aero performance rather than the comfortable, smooth ride of a road bike. Tubing is shaped for minimal wind resistance. Wheels have high, narrow rims for aero performance. Even the spokes are bladed, and many racers perfer solid disc wheels for racing (they catch the cross-winds, though, and aren's suitable as training wheels).
Any road bike can be converted temporarily or permanently to a TT bike. A temporary solution is to attach clip-on aerobars; a permanent solution is to replace the handlebars with TT bars. Depending on the terrain and the strength of the rider, a chainring with a higher tooth count may be a worthwhile investment.