Pure Land Buddhism is the most widely practised form of Buddhism in East Asia by a large margin, and it rests entirely on a promise that a buddha is held to have made and to be keeping.
The account is in the Larger Sukhavativyuha Sutra. A monk named Dharmakara, in the presence of a previous buddha, makes a series of vows and declares that he will not accept buddhahood unless they are all fulfilled. The decisive one, generally numbered the eighteenth, undertakes that beings who sincerely call on him, wishing for birth in his land, will be reborn there. He then attains buddhahood as Amitabha, boundless light, also called Amitayus, boundless life. The logic is compact and is the whole of the tradition: he is a buddha, therefore the vows were fulfilled, therefore the promise holds.
Sukhavati, the land of bliss, in the west, is not a heaven in the sense of a final destination. It is a place where the conditions for practice are perfect and where awakening is therefore assured. The claim is not that calling on Amitabha substitutes for the path; it is that it secures a rebirth in which the path cannot fail.
The practice is recitation of the name: nianfo in Chinese, nembutsu in Japanese, namo Amituofo and namu Amida butsu. It requires no literacy, no monastery, no leisure and no ritual expertise, which is why it spread as it did.
Honen in twelfth-century Japan made exclusive nembutsu the sufficient practice. Shinran, his disciple, took the further step that defines Jodo Shinshu: if the practitioner's own effort could contribute to the result, salvation would be a wage rather than a gift, so even the trust that prompts the recitation must itself be the buddha's gift. On that view the recitation is gratitude for something already accomplished rather than a means of accomplishing it. Shinran married and had children, and the Jodo Shinshu priesthood has been non-celibate since.