The aerodynamic handlebar attachment used in time trialing is called aerobars.
Also known as tri-bars, aerobars use forward extensions and padded elbow rests to place the rider in a tucked position. This reduces frontal area and helps the cyclist cut through the air, which matters greatly in a time trial because riders race alone rather than drafting in a group.
Aerobars became prominent in the late 1980s. Greg LeMond famously used them in the final time trial of the 1989 Tour de France, overcoming a 50-second deficit to Laurent Fignon and winning the race overall by eight seconds. That dramatic result helped make the equipment widely known.
They are not simply another name for drop, bullhorn, or butterfly bars. Aerobars may be bolt-on extensions attached to other handlebars or integrated into a dedicated time-trial cockpit. Because they reduce access to the brakes and can make steering less stable, they are restricted or prohibited in many mass-start races.