In Indian religions such as Hinduism and Buddhism, Deeksha is the ritual of initiation into the worship of some deity by a guru (Deeksha guru) who bestows mantra(s) and takes the karma of the initiate -

raji catmatyaja dosah patni-papam sva-bhartari
tatha sisyartjitam papam guruh prapnoti niscita
Hari Bhakti Vilasa 1.70:
"The faults of the counselor fall on the king, and the sins of a wife fall on her husband. In the same way a spiritual master attains the sins of his disciple. That is certain."

divyam jnanam yato dadyat kuryat papasya sanksayam
tasmad dikseti sa prokta desikais tattva-kovidaih
Deeksha primarily means a transfer of spiritual knowledge. -

Vishnu Yamala (tantra).

"The process that bestows divyam jnanam (transcendental, spiritual knowledge) and destroys sin (paap), the seed of sin and ignorance, is called Deeksha by the spiritual persons who have seen the Truth (desikais tattva-kovidaih)."

tapah pundram tatha nama mantro yagas ca pancamah
ami hi panca-samskarah paramaikanti-hetavah
Vaishnava pancaratrika system requires a sadhaka to undergo the process known as pancha samskaara consisting of pancha (five) stages of samskara (purification):

yatha kancanatam yati kamsyam rasa-vidhanatah
tatha diksa-vidhanena dvijatvam jayate nrnam
"Tapah, pundra, nama, mantra, and yaga; these five items comprise pancha samskara. They are the cause of intense devotion to Lord Hari."

"As bell metal is turned to gold when mixed with mercury in an alchemical process, so one who is properly trained and initiated by a bona fide spiritual master becomes a brahmana immediately."
(Tattva-sagara, Hari-bhakti-vilasa 2.12)

Tantra use different procedures known as Tantric Deeksha.

Another type of Deeksha, into a monastic order, involves a vow of celibacy, renunciation of all personal possessions and of all worldly duties, including family ties. Deeksha has the same meaning in Jainism. Deeksha is also called Charitra or Mahanibhiskraman in Jainism.