Perhaps the best way to introduce medieval Shinto is to discuss it in terms of the traditions that influenced it. Although Buddhism was not the only influential tradition, it was undoubtedly the most important. The Buddhist theory of honji-suijaku (“original substance manifests traces”) pervaded practically the whole of Shinto. The theory of honji-suijaku, transmitted from China to Japan, became the theoretical foundation for considering Japanese kami as “manifest traces” (suijaku) or counterparts of the “original substance” (honji) of particular Buddhas and bodhisattvas. For example, as early as the Nara period, Hachiman was considered both a kami and a bodhisattva without a clear distinction of Shinto or Buddhist identity. In later periods almost every Shinto shrine considered its enshrined kami as the counterpart of some Buddha or Buddhist divinity. It was customary to enshrine statues of these Buddhist counterparts in Shinto shrines, and this practice further encouraged the interaction of Buddhist and Shinto priests. [Japanese Religion, 120-1]
via Honji Suijaku.