An Oral Tradition is a group of stories that somehow define a culture, and have certain characteristics in common. Usually, there are groups of phrases that are repeated within the story to keep the person singing (usually, although it is possible that they may be speaking) if they forget what they’re talking about for a second. In essence, this common language lets the person memorize phrases, so while they’re keeping track of the whole story, they can add these phrases to fill out a line, or just explicate an item further. In the case of the so-called Homeric Greek, which exists only in the epic poems of Ancient Greece, epithets like “Farshooting Apollo” or “Grey-Eyed Athena” are metrically suited to dactylic hexameter and are therefore perfect for filling out a Homeric line. In Old English, Beowulf includes similar repeated phrases, such as: “Beowulf, the son of Ecgtheow, spoke:”. The example from Beowulf is much more specific, as it can only be used before one of his speeches (although that occurs quite frequently in that poem), the examples from Homer are far more versatile, and so if Apollo is speaking, or fighting, or hurtling pestilential arrows, the epithet could be used (although in Homer, that doesn’t usually happen, but I digress)
The point is, an Oral Tradition is basically that, oral and a tradition. Almost all discussion of oral traditions came following the work of Milman Parry, who died before his book was finished, giving every scholar with an opinion a chance to put their two cents in. The fact that his thesis was left unfinished is both a curse and a blessing, as scholars didn’t have to refute his argument first, because he hadn’t actually made one. But there are innumerable volumes of work to sift through if one is mildly interested in the analysis of a modern (or post-modern, or post-post-modern, or now) oral tradition that Parry found in what was then Yugoslavia. Since then, people see evidence of oral traditions everywhere. My personal favorite place is in hip hop, and if you think about it, you can see formula and repetition all over the place there.