Even though this is very broad in nature, I think there is much here to analyze in a free and open manner. You might also find many responses to it. Some of them might be divergent from "traditional answers." This would be where mine resides. I think one of the most interesting aspects of poetry which can be passed down is the use of imagery in poems to illuminate different valences of experience. The idea of truth being a "mobile army of metaphors" is enhanced greatly when imagery is seen as a way to express human experience. The imagery of "for whom the bell tolls" or "wandered lonely as a cloud" is as powerful as "to strive, to seek, to find, and not to yield" or "Does it explode." Over time, the employment of imagery and image- ladened language is what allows poetry to be fully appreciated, acquiring a greater level of meaning over time.
Poetry is 'memorable speech' said W. H. Auden. The handing down to posterity has always been considered as a high-art criterion. From Matthew Arnold's classification of Literature of Knowledge and Literature of Power and even before, universality is held up as the hallmark of great literature, great poetry included.
The truths presented to by a great poem are always of a general and timeless nature, even if it is a context-bound and specific poem with contemporary issues. Poetry inductively touches the generic experience of mankind--universal phenomena like love, relationships, birth, death, thought-processes, psychic states. These fundamental aspects are surely handed down. Apart from the content what one remembers is its rhythm, style and language. The poets are the makers as well as evolvers of a language and poetry in many way creates the future of a language; its innovations are incorporated into the language with the passage of time.