In mythology Jimmu was a descendant of the Sun Goddess, Amaterasu. Ugayafukiaezu no Mikoto, a Kami (a god) is his father. Considering that both of these people are gods, it is unlikely that he was a real person. But that's the short answer. The long answer is a bit more in depth:

The Japanese migrated to the Japanese Islands, that much is known but it's not known when or from where (though probably from Korea and that region). Largely the Japanese were concentrated in the south and seem to have been organized in small villages during what is known as the Yayoi and Kofun Periods. During the end of the Kofun and the beginning of the Asuka Period, the villages became more fortified and larger, and local leaders developed into clans known in Japanese as Uji.

Officially, the Uji are unified under the Yamato Family by the eight century C.E. As the Yamato claim descent from the Sun Goddess, this is probably where the idea of Jimmu comes from. The Japanese State seems to just sort of...happened, and like all states that seem to come out of nowhere, they invented a mythological history for themselves as an easy way to explain what was most likely a convoluted series of wars and deals for Yamato hegemony. Rather than recalling all the conflict that undoubtedly took place, Jimmu becomes an easy way to explain unification. Who established the armies? Jimmu. Who unified the clans? Jimmu. See where I'm going with this?

In all reality though, what the myth of Jimmu represents is a case where mythology has preserved actual history (we see this in cases like Romulus, and Hercules, indeed if you live in America Washington seems to very very slowly be moving towards this). A local strongman may have had enough strength and guile to begin unification, who was then mythologized as Jimmu. Or perhaps he, like Prince Yamato, is an example of a blending of various stock characters in order to explain the past.

I hope this helped answer your question!