Elrond is the keeper of the Last Homely House in the lovely valley of Rivendell. He is also half-elf, half-man – "In those days of our tale there were still some people who had both elves and heroes of the North for ancestors," and Elrond is one of these. Like Gandalf, he's a character of great wisdom and legendary importance who has a very small role in The Hobbit and a much bigger part in The Lord of the Rings. And also like Gandalf, Tolkien leaves us a lot of room to imagine Elrond's place in Tolkien's larger folklore:
[Elrond] was as noble and as fair in face as an elf-lord, as strong as a warrior, as wise as a wizard, as venerable as a king of dwarves, and as kind as summer. He comes into many tales, but his part in the story of Bilbo's great adventure is only a small one. (3.28)
By mentioning the fact that Elrond "comes into many tales," Tolkien is gesturing to a much larger folklore tradition of his own, in which Elrond plays a large part. In The Hobbit, Elrond is mainly around to give Bilbo a refuge at both the beginning and the end of his adventure. And it's also Elrond who points out to Thorin & Co. that their map of the Lonely Mountain has some special hidden runes. These runes, which are only visible under moonlight, say that the side door will open on the last day of autumn, Durin's Day. So that's helpful news. But we'll have to consult The Lord of the Rings to know more about Elrond Half-Elven.