The speaker in the poem "Ode on a Grecian Urn" is fascinated and teased by the figures on the urn. All the figures are frozen in time and therefore they exist in an eternal state. But, in being frozen, the figures are cold and lifeless. The depictions on the urn represent a paradox: they are eternal and their moods and emotions are frozen forever, but they are lifeless at least in the sense of existing in time and involving the five senses.
The speaker is obsessed with the figures on the urn and the paradox that they symbolize for him. Consider the second stanza. Melodies you can hear with the ear are sweet but the unheard melodies on the urn are sweeter because they are eternal and not subject to error in real existence. Likewise, the trees will never lose their leaves. And while the lover will never be able to kiss his beloved, she will always be near him and always be beautiful. This is important, concerning beauty, because the notions of time, beauty, and truth conclude the poem:
Bold lover, never, never canst thou kiss,
Though winning near the goal--yet, do not grieve;
She cannot fade, though thou has not thy bliss,
For ever wilt thou love, and she be fair!
In the last stanza, the speaker remarks that he is teased by these eternal, frozen images of life. But then he also claims "Cold Pastoral!" This hints at the possibility that the speaker realizes that these images of life frozen eternally in perfection, actually only represent temporal fragments, not eternal forms. In the last lines, the speaker considers what the personified urn might say:
Than ours, a friend to man, to whom thou say'st,
"Beauty is truth, truth beauty," --that is all
Ye know on earth, and all ye need to know.
The speaker says to the urn that in future generations the urn will say "Beauty is truth, truth beauty." In the next lines, it is unclear who "ye" is, but one logical interpretation is that the speaker is talking to the urn, so the urn is "ye." What this means is that for the (personified) urn, beauty and truth are simple; beauty and truth are based on aesthetics and symbols, two-dimensional pictures which may or may not represent truth and beauty. That is the assessment of truth and beauty in the world of the urn, so that is all the urn ("ye") needs to know. For the speaker, and all humans living in the real, linear world, truth and beauty are more difficult to describe and experience.
In reality, that "bold lover" has to chase his beloved. There is a journey toward truth and beauty. From this interpretation, the conclusion is that, in real life (unlike the "world" of the urn and its figures), beauty and truth are not interchangeable and they do not come easily. Thus, we must pursue these virtues "in midst of other woe."