Short answers, pulled from the story.
Transfer of merit (pariṇāmanā or pattidāna) is a Buddhist practice in which a practitioner mentally dedicates the merit from good deeds to deceased relatives, deities, or all sentient beings. The recipient can receive the merit if they rejoice in the meritorious acts of the giver, and the giver's own merit is not diminished in the process.
King Bimbisāra is the central figure in the oldest recorded example of merit transfer, found in the commentaries to the Pāli Tipiṭaka. According to the story, the Buddha instructed Bimbisāra to give food and cloth to the monastic community and transfer the merit of those gifts to his former relatives who had been reborn as pretas, hungry ghosts; the pretas then received the objects given to the monks.
Scholars have long noted the tension, since Buddhist karma holds that karmic results are experienced solely by the person who performed the original action. Indologist Richard Gombrich argued that later commentators resolved the conflict by reinterpreting the Pāli term anumodana from 'giving thanks' to 'rejoicing,' allowing the deceased to be seen as making their own merit through rejoicing rather than passively receiving another's merit.
Scholars disagree on the date. Indologist Heinz Bechert placed the fully developed doctrine between the fifth and seventh century CE. Indologist Richard Gombrich traced its origins to around the fourth century BCE, and Buddhist Studies scholar Gregory Schopen found evidence of merit transfer in Buddhist inscriptions as early as the third century BCE.
The monastic community, the Saṅgha, serves as an intermediary between devotees and their deceased relatives. It is understood as a 'field of merit,' a worthy recipient whose presence helps donors accrue the merit required for transfer. Donations to the Saṅgha are the primary vehicle through which merit is generated and then dedicated to the deceased.
In Japan, some temples are called ekōdera, meaning a temple for merit transfer, and the practice is usually led by married priests rather than the celibate Saṅgha. A special memorial service called Mizuko kuyō is often held after an abortion to dedicate merit to the spirit of the deceased child. The Jōdo Shinshū school rejects merit transfer on doctrinal grounds, though exceptions occur, and the religious leader Nichiren (1222-1282) considered it ineffective.