HESH stands for H
ead. It is a type of anti-tank
warhead. It is for use in weapons that cannot muster the energy
required to use kinetic
shot, nor the precision and/or weight required for a HEAT
round large enough to penetrate a target.
For a brief period in the 1960s and 1970s, some main battle tanks did not mount guns of sufficient strength to penetrate opposing tanks' armor by these conventional means. HESH was invented as an alternative. Its success is of lower probability; but some chance is better than none. A HESH round consists of a deformable, sticky chunk of plastic explosive with a fusing system. When fired at a tank, it hits the armor and 'squashes', spreading itself out across the surface of the armor into a thin sheet. At that point, the fuse detonates it. Although unable to penetrate the armor, it sends shock waves from the blast into the armor itself. On the inside of the armor plate, this energy is released in the form of fast-moving fragments from the interior surface of the armor as energy from the explosion alternately violently compresses and expands the armor longintudinally. These fragments of armor rip through whatever is behind the armor and ricochet about the tank crew compartment like a large cloud of high-velocity buckshot. For an example of this principle, see the popular desk toy consisting of four metal balls on string (which rootbeer277 helpfully informs me is called a Newton's Cradle); releasing the end ball to slam into the other three causes the ball at the other end to fly off with equal force. In this case, the 'slam' is hard enough to break the string that holds the last ball on (molecular bonding). This release of energetic fragments is called spalling.
In addition, this warhead is still used in low-velocity delivery systems such as man-portable rockets and recoilless rifles. Examples of the latter include the Armbrust disposable LAW or the U.S. AT-4.
One source that collects much of the historical record on tanks vs. antitank arms is Tank Killing, by Ian Hogg. Mr. Hogg is an editor for Jane's Information Group where he specializes in armored vehicles. For references to current usage of the acronym, see the any U.S. Army pub, such as this one available from Ft. Leavenworth (it's a glossary).