It's natural to wonder how anyone could possibly have been expected to remember the entirety of The Odyssey. After all, the poem existed in the oral tradition long before it was ever written down -- thousands of lines of verse were passed down from generation to generation by mere word of mouth. Looking at the sheer volume of words in a work like The Odyssey, how might we suppose it actually feasible for one person to recite the work from memory?
You may notice in reading The Odyssey that the epic seems rather repetitive and formulaic in its structure. This is no accident: in addition to the aesthetic function of giving the epic a lyrical quality, the structural repetitiveness functions as a type of mnemonic device to facilitate easy memorization and recall in the Bard performing the poem orally. This happens both in the microcosm and in the macrocosm of the work: in the case of the former, particular lines and phrases appear ad nauseam over the course of the work; in the case of the latter, the same basic structure of events (feasting, sleeping, etc.) appears many times over the course of Odysseus' journey, adding a level of similarity to the many places he visits on his quest homeward. For example, to cite Martin Mueller of Northwestern University (see bibliography for reference): there are 32 instances of phrases about "rosy-fingered Dawn" in the Odyssey, virtually always used to introduce the dawn of a new day -- this is an example of repetition in the microcosm. Furthermore, there are five repeated passages describing Odysseus' companions following orders to get into a boat, sit down, and beat the gray sea with their oars -- this is an example of repetition in the macrocosm.
Beyond its pragmatic function as a mnemonic device, this structural repetition makes the poem feel like something of a tapestry, with repeated patterns intricately woven together in order to create a work that is greater than the sum of its parts. It is reminiscent in this way of the mathematical function of fractals, wherein one or two atomic patterns are repeated to very high degrees, creating patterns that repeat both on microcosmic and macrocosmic scales (see the pyramid picture for an example of this). Not only, then, is The Odyssey beautiful by virtue of its story or lyrical lines alone: the structure itself reveals another, subtler thread of beauty that unifies the vast poem into a single object that one can potentially commit to memory.