Most bombs consist of a metal case filled with explosives like TNT or RDX and a means of detonating the contents. By contrast, a fuel-air bomb is filled with a highly combustible fuel in either liquid or gel form. The fuel may be as exotic as aluminum powder or as simple as petrol. Detonating this device is like lighting a match in a gas-filled room. A small charge in front of the bomb or warhead releases fuel, which mixes with the air to form vapor cloud. Immediately thereafter, a detonator at the rear of the bomb triggers the midair explosion over the target as shown in the image above.
The United States used fuel-air bombs in Vietnam War to obliterate the targeted jungle area and clear away mines and booby traps. When used against mass troops and enemy fortification, such bombs would simply liquidate them with both a fireball and concussion. They would burst eardrums, rapture internal organs and collapse the lungs of troops further away. It's not without justification that these explosive devices are often called a poor man's atomic bombs, though the blast and the shock they produce is still only a fraction of that of a tactical nuclear weapon. However, they do have one advantage: there is no radiation in fuel-air bomb.
Here's a Discovery Channel video (from YouTube) of fuel-air explosive. Note that HBA is not affiliated with creators of this video.
Fuel-air explosive (Wikipedia)