In Doctor Who, psionics is the study of psychic powers. Psychic powers themselves come about through an innate ability to manipulate three special forces which have not been tapped (and, indeed, are largely unknown) to Tech Level 5 science: artron energy, the lifeforce and fictional energy.
Artron energy is generated within (or by) the space-time vortex, and is difficult to fully understand even for a Tech Level 9 civilization. Creatures that pass through the vortex gather artron energy around them, and artron energy can escape through thin points in space-time where the vortex is closer, as well as actual rifts in the fabric of the universe. The rift in Cardiff, and the Untempered Schism on Gallifrey, leak artron energy. Individuals who grow up close to those rifts — or who are strongly exposed to them as children — sometimes develop psychic powers.
The lifeforce is energy generated by all living things, infused with the living down to the molecular level. The degree to which the lifeforce interacts with a potentially living thing is the difference between being alive or being dead. Yet, even dead creatures that were once alive maintain reserves of this energy for a long time, or their bodies would collapse into a fine powder.
Fictional energy is a 6th dimensional energy source, which is directly related to probability and creativity. Fictional energy is not fully understood even at Tech Level 10, except perhaps by creatures such as the Guardians of Time and the Trickster. All storytelling and imagination utilize fictional energy, but massive uses of fictional energy to create psychic effects usually require very powerful psychics (and can create ionic discharges).
These energy types interact with each other.
The lifeforce and artron energy are entangled (similarly to the way in which quantum particles can be entangled, but with a more widespread and far-reaching implications) but, unlike quantum particles, have properties that can be decoded or programmed by their connections to fictional energy.
In some cases, primitive creatures devise rituals in order to harness fictional energy to encode, decode, and manipulate these energies. The science of psionics seeks not only to interpret the purposes of these rituals, but also to understand, harness, and manipulate these energies without the constraints or uneven results of ritual.
As with every type of energy, creatures have evolved to consume artron energy, fictional energy, and even to consume the lifeforce directly, although these creatures are thankfully rare, and usually come from (or have access to) other dimensions or universes.
True artificial intelligence requires a connection to the lifeforce, and allows the intelligence to potentially access psychic powers (as with BOSS and WOTAN).
At Tech Level 7, it is possible to create materials that can hold or react to the lifeforce and artron energy (even if artron energy is not fully understood), thus enabling the creation of products such as psychic paper and the telepathic pendants of the Arcateen.