Basic Information
HESH, standing for High Explosive Squash Head, is a form of shaped charge armour piercing round, generally found in ordnance calibres only. This sort of ammunition is sometimes also called HEP (High Explosive Plastic) and similar things.
The round works by delivering a significant charge of plastic explosive to the target with a base impact detenator - thus the soft mass of the charge flattens itself against the target's armour plate before being detonated. When the charge is fired, a phenomenon similar to the Misznay-Schardin effect propagates a shockwave through the plate that will either collapse it (if it is weak enough) or, failing that, flake particles of spall from the inside and send them flying about the inside of the fighting compartment.
This type of ammunition was developed in Britain in 1940, and was briefly popular amongst UK forces and several other nations, especially those who purchased the Centurion MBT. Currently, HESH is in decline as an armour piercing round since it is almost completely ineffective against either non-homogenous armour, or any form of spaced armour since neither will propagate a shockwave effectively. Even vehicles with homogenous armour can have their resistance to HESH greatly improved by fitting a protective liner - usually made from some kind of ballistic cloth - to adsorb spall fragments.
That said, HESH remains a relatively useful general purpose round - it remains useful against unarmoured targets and against battlefield fortifications (which was, ironically, the first major role in which it was deployed) and (in tank cannon calibres at least) is quite capable of demolishing many lightly armoured vehicles.
HESH has also been historically preferred for use in rifled tank cannon, given that until very recently HEAT rounds were undermined by spin-stabilisation. This problem has since been overcome - and in any case, rifled cannon are less and less popular for tank use.