‘Adhishthana’ means power of the Buddha. The Lankavatara sutra describes it thus:

“…sustained in two ways by the power (adhishthana) of the Buddhas… What are the two ways? __ One is the way a Bodhisattva is made to attain states of mental tranquillisation, and the other is that by which the Buddha personally appears before the Bodhisattva and anoints him with his own hands.”

The Lankavatara further states that, “it is thus due to the power of the Buddha (adhishthana) that the Bodhisattva at the first stage attains the Samadhi known as the Light of the Mahayana and that having attained this [he] finds himself now blessed by the personal presence of all the Buddhas…”

The Lankavatara then goes on to explain that it is through the power of the Buddha that the later stages are also obtained.  D.T Suzuki described it thus:

“The Buddha is creative life itself, he creates himself in innumerable forms with all the means native to him. This is called his adhisthana, as it were, emanating from his personality.  The idea of Adhisthana is one of the Mahayana landmarks in the history of Indian Buddhism and it is at the same time the beginning of the ‘other-power’ (tariki in Japanese) school as distinguished from the ‘self-power’ (jiriki).”

REFERENCE
Suzuki, D. T. “The Shin Sect of Buddhism”. www.nembutsu.info. Journal of Shin Buddhism. http://www.nembutsu.info/suzuki1.htm [accessed 9th of July 2017]