Psionics are the ability of using the mind to induce paranormal phenomena. It is present to various degrees in various species.
The presence of psionic powers within a species is rare, and is dictated by their structural makeup. Even the subtlest of changes to an organism's (or species') genetic code can destroy its psionic potential. Psionic emanations can be lethal to organisms, and are not yet fully understood by terran science.
The Khala is a structured approach to protoss psionics. It was developed near the end of the Aeon of Strife in order to restore the sanity of the protoss.
The Khala grants much control and discipline over psionic power. Being subsumed in the Khala meant a certain loss of self in addition to the gain of the "other". There was a risk the loss could be drastic. Most Judicators and Templar subsume themselves into the Khala at least once a day.
The fortitude of the Khala protects protoss from assimilation by the zerg or other corruptive/virulent influences.
Beings linked to the Void have modified Psionics known as Void Powers, in which the Void mixes into their Psionic abilities, causing different effects, and giving them unique abilities.
The Void provides the Nerazim with enormously strong individual will and enabled them to learn cloaking powers very quickly.
The Tal'darim also wield energies from the Void. These powers are enhanced by their exposure to terrazine, which weakens the barrier between material reality and the Void.
It is for reasons like this that those linked to the Void have, in the past, been mistaken for Psykers, as some civilizations either cannot find, or outright disregard, the difference between The Warp and the Void.
Psionicists and Psykers
Psionics, while in some ways similar, are drastically different powers from Warp Powers, due to differences in origin, with Warp Power users, also called Psykers, drawing power from the Warp. While some Psionicists gain powers from the Void, their actual power comes from the mind, with the Void merely influencing what happens to the energy they wield.