We understand that the sunflowers are symbolic of the elderly as a result of lines such as, "they have wonderful stories / of when they were young." Even the description of their faces as "burnished disks" and their "dry spines [that] / creak like ship masts" helps us to realize that Oliver is talking about older people whose faces have been shined by the sun and whose bones have become more brittle with age.
One theme of this poem is that there is beauty in age. To describe old folks, first of all, as sunflowers—such happy-looking flowers that are associated with the sun, one of the sources of our life itself—begins to illuminate this idea. Their faces are "bright" and they "follow the sun;" their lives are "a celebration" and they "hope for a deeper acquaintance" with all of us. These are all such incredibly positive, joyful descriptions that we realize, with the speaker, the beauty in these individuals.
Another theme is that there is no less life in the old than there is in the young. The speaker describes their "green leaves, / so heavy and many," perhaps making us think of the youth often associated with the color green—there is life in these individuals yet. They are verdant and growing, even if the young have trouble seeing it. Further, their roots seem to be "so uprightly burning;" it is as if they have imbibed some of the sun itself that they can "burn" with such life.