The on-hit: cast spell item property causes a spell to be fired on-hit, either when the wielder scores a hit (for weapons) or when the wearer is hit (for armor). The possessor of the item is considered the caster, and the other creature is the target of the spell. The caster level is listed as the "level" of the property. The usual spells can be associated with this property, as can a few "spells" specifically designed solely for use as an on-hit property (e.g. chaos shield). The latter are technically spells (as are many special abilities in the game), but they are better understood as item properties.
There are a few other on-hit properties that mimic this property for specific spells (e.g. "on-hit: lesser dispelling" mimics "on-hit: cast spell: lesser dispel"). Such properties are distinct properties that function slightly differently, but in many cases the distinctions are of little importance to players. (The main reason these other properties exist is that they predate "on-hit: cast spell".) Perhaps the most significant distinction is that at most one "on-hit: cast spell" property will ever be fired for a single hit, even if multiple such properties exist (hence the reason darkfire and flame weapon do not stack). Other types of on-hit properties may also fire though, including those that mimic "on-hit: cast spell". Another distinction involves the frequency with which these properties are triggered. "On-hit: cast spell" is triggered with every hit while other on-hit properties are triggered about half the time, unless otherwise specified in the property name.
This item property gives module builders great flexibility in designing items, but such flexibility comes at a price. Most spells were designed under the assumption that a character could cast at most two spells in a round. When it is triggered on-hit, however, a spell can be cast much more often, potentially ten times per round. Injudicious use of this item property can cause the game to lag.