In this poem, the speaker is making observations about eternal beauty vs real life and aging. He is addressing the urn directly when he says "thou."
While observing a beautiful Grecian urn, the speaker can see images of young lovers about to embrace, a musician ready to play music, sylvan images that are lush and green, among other images frozen in time. The speaker realizes the setbacks of being alive with the prospect of passing time. Exemplified in the lines:
Heard melodies are sweet, but those unheard / are sweeter
the speaker observes that while life as time passes, or the melody we hear, is beautiful, the prospect of beauty and melodies yet to come brings a promise of hope that within the urn will never fade. While the young lover on the urn is near his beloved, he cannot quite touch, kiss, and embrace her. However, the speaker points out that the young man should not grieve, because his beloved's youth and beauty will never fade, and that perfect moment of being in love and about to embrace is eternal for him. Likewise, the rest of the poem tells that while the people on the urn cannot live life and enjoy the beauty, their life will remain frozen and within that beauty forever. The passing of time will never affect the people frozen on the urn.
On the other hand, the speaker observes that real life continues outside the urn:
When old age shall this generation waste,
Thou shalt remain, in midst of other woe
When the speaker, and everyone else alive's, time comes to age and die, the urn will remain with its beauty long after. The people pictured on the urn will stay young, beautiful, and forever in the same moment. However, the speaker does add that while we, in real life, will age and die, the urn will also remain in its own woe. The urns beauty will never die, but those people will never experience the joy real life can bring. The young lover will never embrace his beloved, the musician's sweet melody will never be heard, and those people frozen in time will miss out on the joy of life.
The speaker brings to mind the argument of whether it is better to have eternal youth and beauty, but miss out on the joys of life, or to have life, love, and joy, but know that sooner or later you will age, grow weaker, and eventually die.