PSIONICS
In the StarCraft Universe, psionics is a way of saying "psychic powers." Every species in the universe is capable of having them. The Protoss and Hybrids have the highest amount of psionics, where the Terrans have a low population that are actually psychic. The Zerg are controlled by telepathy. This is namely by the Overmind and then later Kerrigan as the Queen of Blades.
In Terrans, there are two types of psionic powers: telepathy and telekinesis. It is extremely rare for a terran to possess both. Once the Confederacy, pre-StarCraft, noticed the powers manifesting, they started what is called the Ghost Program. The Ghosts are assassins, conditioned and trained to use their psionic abilities to kill on behalf of the Confederacy. Children are tested at birth for these abilities, and if they are found to have them, are taken into the Ghost Program. The Fringe Worlds (aka: the worlds on the outer reaches of the Confederate power base) have a lower test rate, given how almost Old West they are. After the Sons of Korhal destroyed the Confederacy, and became the Dominion, Emperor Arcterus Mengsk reactivated the Ghost Program with more vigor than ever.
Psionic powers for the Terrans relate to a Psi Index. It is a rating system created by the Confederacy, used by the Dominion, to scale how powerful the person is with their psionic abilities. It scales 1-10. After the Ghost Program found Sarah Kerrigan, the Psi Index had to be completely reorganized in order to accommodate her power. The table is as follows:
1-2 No psychic abilities.
3-5 Limited abilities.
5-8 Telepathic abilities.
8-10 Possible telekinetic abilities. Rare.
Most Ghosts are between 5-8. However, both Sarah Kerrigan and Nova Terra scale in the 8-10 range. It should be noted that as of StarCraft II: Wings of Liberty, Kerrigan - as the Queen of Blades - is registered as a Level 12 Psionic Being. In Heart of the Swarm, due to being de-infested, Kerrigan is registered as a Level 11.
TELEPATHY
Telepathy works a tad differently in the StarCraft universe than it tends to in other canons. For terrans with telepathic powers, very few of them can block the thoughts of others. It is capable with training, or with implants placed in side the head to lessen the amount of input, but generally there is no way of blocking them out. Kerrigan herself had implants placed inside her head, left in on her request, that kept her from "going insane." Range or depth is not necessarily stated, but it's safe to assume that it can be either a great radius or a small radius, depending on what is needed for the Ghost to find it's target.
As for some non-psychics, some humans have the ability to shield their thoughts. This is most likely due to extensive training.
MANIFESTATIONS
Outside of just mind-reading and throwing objects, Ghosts can manifest their abilities in other ways. When they are in their environmental suit, they can use their psionic energy to cloak themselves. People who are sensitive to psionic powers can sense them, as well as devices that are designed to detect them. Depending on how much energy they can expend is how long a Ghost can remain cloaked. They can also use their powers to enhance their eyesight to see through walls to follow their target. Ghosts are capable of focusing their powers into an EMP shot that will knock out other psionic shields as of StarCraft II.
They are also able to "Lockdown" on robotic and mechanical structures, meaning that for the duration they are unable to be used. As of StarCraft II, psionic studies led to the creation of a Psi Augmenter that is installed in certain suits. These allow a Ghost to remain cloaked indefinitely. All of the abilities a Ghost utilizes is through their training. Kerrigan, after removing her Ghost programing after becoming a Terran-Zerg hybrid, was able to expand her own psionic abilities and use abilities that are more along the lines of what a Protoss can use.
SOURCES:
-
Psionic Powers @ SC Wikia-
Ghost Unit @ SC Wikia-
Ghost Unit (SC: Ghost) @ SC Wikia-
Ghost Unit (SCII) @ SC Wikia-
Sarah Kerrigan @ SC Wikia-
Psionic Index @ SC Wikia