Non-corporeal refers to anything that does not possess material substance in the physical plane. In the context of Gemstone, it is usually in reference to various creature, often undead, which are insubstantial and possess only a spiritual or ghostly form. Creatures such as this have a number of factors that cause them to be different in combat than regular creatures. Usually, they cannot be killed by a critical injury, they do not take wounds from damage, and some types of attack are less effective or entirely ineffective at injuring them. Many of these creatures will evaporate quickly after death, much faster than the usual natural creature decay.
The sorcerer's Phase (704) spell possesses a feature that forces non-corporeal creatures into physical form, which subjects them to the normal limitations and weaknesses that corporeal creatures have.
Disintegrate (705) is particularly powerful when used against non-corporeal creatures, actually stronger than when normally used against corporeal creatures.
Kai's Smite is obtained at the twenty first step of the Order of Voln. This attack is activated via the SMITE (verb) and NOT by invoking the symbol. When the attack connects with a non-corporeal creature, instead of doing damage, it will temporarily corporealize it.