How does the contemplation of a Grecian urn relate to the subject of the poem in "Ode on a Grecian Urn?
Throughout the poem the urn functions as a symbol of eternity which is compared against the brief and transitory state of man's existence on the planet. Note how the speaker of the poem refers to the urn in the first stanza:
Thou still unravished bride of quietness,
Thou foster child of silence and slow time,
These images have been carefully chosen to emphasise the way that the urn that is being contemplated is undamaged by the ravages of time and how it preserves history. Thus it is that this urn and the scenes that the speaker views on it triggers off a series of reflections about beauty, art and mortality, that are expressed in the last stanza. However, there is a crucial ambiguity that is created in this stanza that is never resolved. We are left unsure as to whether the urn is being celebrated as a symbol of the eternal nature or art and beauty, or whether it is used to make a critical comment on the limitations of art and the need to turn to life rather than idealised expressions of beauty. Consider the following quote:
When old age shall this generation waste,
Thous shalt remain, in midst of other woe
Than ours, a friend to man, to whom tho say'st,
"Beauty is truth, truth beauty"--that is all
Ye know on earth, and all ye need to know.
Note how both the positives and negatives of contemplating the urn as an ideal of art and beauty are explored. On the one hand, such a contemplation gives us a sense of the the timeless nature of art. On the other hand, this contemplation only exacerbates our awareness of our own mortality and eventual death.
Thus you might find it helpful to consider what the urn symbolises in the poem, and the author's ambivalent attitude towards the symbolic meaning.