The popular formulation is that a bodhisattva refuses to enter nirvana until every other being has been liberated. It is a moving idea and it is a simplification, sometimes a confusion.
What the texts more often describe is a being who, having attained the insight that would permit departure from the round of rebirth, remains engaged with the world by choice, sustained by vow and by compassion rather than driven by karma. On the Mahayana account the full awakening of a Buddha is not a withdrawal at all: the doctrine of the three bodies holds that a Buddha continues to manifest and to act for beings after awakening, so there is nothing to postpone. Some schools do describe a deliberate deferral, and the vow of Kshitigarbha is stated in exactly those terms; but a general rule that Buddhahood is refused until the last being is saved would make Buddhahood impossible, and the tradition does not teach that.
The bodhisattva vow is Mahayana's defining commitment across otherwise very different schools. Zen practitioners chant it daily in the form beginning beings are numberless, I vow to save them. Tibetan traditions treat its cultivation as the foundation on which tantric practice is built. Pure Land devotion rests on the vows of a bodhisattva who became the Buddha Amitabha.
Comparisons with other traditions should be handled with care. The bodhisattva is not a saviour in the Christian sense: he does not atone, and beings are not saved by his death but assisted on a path they must walk. Nor is he a divine descent like a Hindu avatar, which is a deity taking form; a bodhisattva is a being working upward, and the categories move in opposite directions. The closest genuine parallel is functional rather than doctrinal: like the saints of Catholic and Orthodox devotion, bodhisattvas are appealed to for help, and their surplus merit is understood to be available to others.