What is Abhinya, the super-knowledge ?

Abhinya or abhiññā (Thai = อภิญญา) , is a Pali word, means super-knowledge, supernatural powers, psychic powers, insights. In Buddhism, the Ariya (the Noble ones) who has developed his/her mind above lay persons, who has sufficient Samatha meditaion training (in the 8 absorptions, the 8 Jhanā), can access the powers in 6 categories. The abhiññā of 6 categories is called chaḷabhiññā ( chaḷa = 6, Thai = ฉฬภิญโญ , ฉฬภิญญา , อภิญญา ๖), is considered Lokuttara (supramundane, above the worlds, transcendental, Thai = โลกุตตระ , โลกุตระ).

It should be noted that not all Ariya persons have abhiññā. During Buddha's time, in one of his sermons, he clearly declared, of the 500 Ariya monks in the audience, only 60 had chaḷabhiññā, having the 6 knowledge and ability.

Since the Buddha emphasized on purification of the mind to get away from mental suffering and access Nibbāna (Nirvāna), so that his students and follower eliminate mental defilements completely, and thus attaining Arahat, he did not emphasize abhiññā.  In addition, he discouraged showing off of abhiññā powers since people might be attracted to it and not practicing "the right path"and "the middle way".  Developing the mind to Ariya states and ultimately Arahat mainly needs Vipassana meditation, most of his monks and layman followers did not have sufficient Samatha meditation training, i.e. mostly they practice upto only 4 physical Jhanā, thus the majority of his followers don't have chaḷabhiññā capability. Stories in some suttas of the Tipitaka (the Buddhist scriptures) list names of monks which Buddha praised as the top experts in some of these categories as evidence of existence of these 'paranormal' powers.

The 6 categories of super knowledge are:-

iddhividhā = magical powers (including psychokinesis, telekinesis, teleportation, flying, multiplicity, etc.)  (The Thai word of iddhividhā is อิทธิวิธี .)

dibbasota = divine ear, hearing from a very far distance. (The Thai word is ทิพยโสต .)

cetopariyañāṇa = penetration of the minds of others, telepathy. (The Thai word is เจโตปริยญาณ .)

pubbenivāsānussati = remembrance of former existence (incarnation, lives) and reincarnation history of others, retrocognition. (The Thai word is ปุพเพนิวาสานุสติญาณ .)

dibbacakkhu = divine eye, precognition, clairvoyance, apparitional experience, seeing the future, but only the Buddha has the unlimited capability level regarded as omniscience, or know-all. (The Thai word is ทิพยจักขุ .)

asavakkhayañāṇa = knowledge of the exhaustion of all mental intoxicants, upon entering various ariya stages, until reaching the fourth Ariya stage, the Arahat. (The Thai word is อาสวักขยญาณ .)

Lay persons with abundant mental defilements, still attached to greeds or desires (lobho / lobha, including rāga, sexual desires), angers (doso / dosa), delusion (moho / moha) with strenuous meditation training in the 8 Jhanā can access only 5 of the 6. They lack the last one which is the most important, asavakkhayañāṇa. The first 5 powers attainable by laymen is called Lokiyaabhiññā (abhiññā of the mundane, worldly level). That explains why some yogi, brahmins, and followers of other faiths who practice meditations have mental powers as well.