(Sanskrit सिद्धि) Literally, "success; any unusual skill, faculty or capability." Nowadays this term usually indicates "spiritual powers." Many of the powers (siddhis) of yoga are related to the "Jinn state," the condition that results from moving physical matter into the fourth dimension.
"The yogi acquires multiple powers (siddhis) in accordance with the awakening of superlative consciousness... Powers [siddhis] are flowers of the soul that sprout when we have sanctified ourselves. For each step that we walk in the development of the chakras, we must also walk a thousand steps in sanctity." —Samael Aun Weor, Kabbalah of the Mayan Mysteries
"If there is Shuddhi (purification), Siddhi (perfection) will come by itself. Siddhi is not possible without Shuddhi." - Swami Sivananda, Kundalini Yoga
"Siddhi is produced by sadhana [practice, effort]. The former term, which literally means "success," includes accomplishment, achievement, success, and fruition of all kinds. A person may thus gain siddhi in speech, siddhi in mantra, etc. A person is siddha also who has perfected his spiritual development. The various powers attainable – namely, anima, mahima, laghima, garima, prapti, prakamya, ishitva, vashitva, the powers of becoming small, great, light, heavy, attaining what one wills, and the like – are known as the eight siddhi. The thirty-ninth chapter of the Brahmavaivarta Purana mentions eighteen kinds, but there are many others, including such minor accomplishments as nakhadarpana siddhi or "nail-gazing." The great siddhi is spiritual perfection. Even the mighty powers of the "eight siddhi" are known as the "lesser siddhi," since the greatest of all siddhi is full liberation (mahanirvana) from the bonds of phenomenal life and union with the Paramatma, which is the supreme object (paramartha) to be attained through human birth." - Arthur Avalon, Mahanirvana Tantra, Tantra of the Great Liberation 
"An accomplished Purnayogi in the path of Kundalini Yoga is in possession of eight major Siddhis, viz., Anima, Mahima, Laghima, Garima, Prapti, Prakamya, Vasitvam and Ishitvam.
1. Anima: The Yogi can become as minute as he pleases.
2. Mahima: This is the opposite of Anima. He can become as big as he likes. He can make his body assume a very large size. He can fill up the whole universe. He can assume a Virat Svarupa.
3. Laghima: He can make his body as light as cotton or feather. Vayustambhanam is done through this Siddhi. In Jalastambhanam also the power is exercised to a very small degree. The body is rendered light by Plavini Pranayama. The Yogi produces a diminution of his specific gravity by swallowing large draughts of air. The Yogi travels in the sky with the help of this Siddhi. He can travel thousands of miles in a minute.
4. Garima: This is the opposite of Laghima. In this the Yogi acquires an increase of specific gravity. He can make the body as heavy as a mountain by swallowing draughts of air.
5. Prapti: The Yogi standing on the earth can touch the highest things. He can touch the sun or the moon or the sky. Through this Siddhi the Yogi attains his desired objects and supernatural powers. He acquires the power of predicting future events, the power of clairvoyance, clairaudience, telepathy, thought-reading, etc. He can understand the languages of the beasts and birds. He can understand unknown languages also. He can cure all diseases.
6. Prakamya: He can dive into the water and can come out at any time he likes. The late Trilinga Swami of Benares used to live for six months underneath the Ganges. It is the process by which a Yogi makes himself invisible sometimes. By some writers it is defined to be the power of entering body of another (Parakaya Pravesh). Sri Sankara entered the body of Raja Amaruka of Benares. Tirumular in Southern India entered the body of a shepherd. Raja Vikramaditya also did this. It is also the power of keeping a youth-like appearance for any length of time. Raja Yayati had this power.
7. Vashitvam: This is the power of taming wild animals and bringing them under control. It is the power of mesmerising persons by the exercise of will and of making them obedient to one’s own wishes and orders. It is the restraint of passions and emotions. It is the power to bring men, women and the elements under subjection.
8. Ishitvam: It is the attainment of divine power. The Yogi becomes the Lord of the universe. The Yogi who has this power can restore life to the dead. Kabir, Tulsidas, Akalkot Swami and others had this power of bringing back life to the dead." - Swami Sivananda, Kundalini Yoga
"Many people are attracted to the practice of Pranayama and other Yogic exercises, as it is through Yoga that psychic healing, telepathy, thought-transference, and other great Siddhis are obtained. If they attain success, they should not remain there alone. The Goal of life is not ‘healing’ and ‘Siddhis’. They should utilise their energy in attaining the Highest.. A Yogi on the appearance of certain Siddhis thinks that he has achieved the highest goal. He may give up his further Sadhana through false contentment. The Yogi who is bent upon getting the highest Samadhi, must reject Siddhis whenever they come. Siddhis are invitations from Devatas. Only by rejecting these Siddhis, one can attain success in Yoga. He who craves for Siddhis is a worldly-minded man. He is a very big householder. Those who crave for Siddhis will never get them. If a Yogic student is tempted to attain Siddhis, his further progress is seriously retarded. He has lost the way." - Swami Sivananda, Kundalini Yoga
"If the [Jinn] practice has been performed well, then your body will enter the “Jinn” state, meaning that it will submerge within the supra-sensible worlds. A body in the “Jinn” state can float in the air (Laghima) or be submerged within the waters (Prakamya), or pass through fire without being burned, or be reduced to the size of an atom (Anima), or be enlarged to the point of touching the sun or the moon with the hand (Mahima). A body submerged within the supra-sensible worlds is submitted to the laws of those worlds. Then, this body is plastic and elastic, so it can change form, decrease its weight (Laghima), or increase its weight (Garima) willingly... The holy eight is the sign of infinity. The two witnesses of the Apocalypse are entwined around the spinal medulla, thus they form the holy eight. All of the mystical powers of the heavenly Jerusalem emanate from this holy eight. Now the devotees can better comprehend why we speak of eight mystical, ineffable powers." - Samael Aun Weor, The Aquarian Message