Psychic power (iddhi) is an ability to act in ways not conforming to the known laws of nature and which is caused by releasing or developing the power of the mind.
The Buddha accepted that some spiritually advanced people can manifest certain psychic abilities and indeed he himself occasionally manifested some of them.
The main psychic powers mentioned in the Buddhist scriptures are telepathy, psychokinesis, levitation and the ability to separate the astral body (manomayakāya)from the physical body.
The Buddha had a cautious attitude towards psychic powers.
The reasons for this were because such powers attract to those who have them enormous reverence, which can easily lead to corruption and also because most who claim to have such powers are actually impostors.
Further, the Buddha felt that having faith in those who have virtue, integrity and mental control is more sound than having faith in those who could levitate or read minds.
Because of this, the Buddha made a rule that if a monk or nun develops such powers they are not allowed to demonstrate them to lay people or tell others of them, without permission of the Saṅgha.
Once a rich man had a valuable sandalwood bowl placed on the top of a bamboo pole erected in the center of town and announced that anyone who could rise up to the top of the pole and take the bowl could have it.
A monk who had developed the ability to levitate took up the challenge and got the bowl after which large crowds of admirers followed him everywhere he went.
When the Buddha heard what had happened he called the monk and rebuked him, saying: ‘You are like a low woman who exposes herself in the market for a miserable coin.’ (Vin.II,110-111).