The poet, who serves as a critic as well - courtesy of the last two lines, thinks of many things: time, love, desire and paradoxes: mortality/immortality, as well as the main dichotomy - or maybe interdepdence is the better word - of life/art.
The images on the urn "tease" the poet because he cannot hear their songs, the trees can never be bare. They are frozen in immortality, as art, these images serve as muses almost: they allow the poet to ask questions about the figures. He wonders what the songs sound like, the frozen image of one chasing a lover (so, never having her -always longing). These are everyday things: nature, ritual, courtship and music.
The poet is teased by wanting to know the outcome of their songs stories, the courtship, etc. So, the poet longs to know as those figures long (longed) to be heard. This is all set to the idea of desire. "Thou still unravished bride of quietness." Still meaning ongoing as well as motionless: frozen in immortality (but in an additional sense of dead since the images are not moving and silent). This paradox of the immortality within art is one thing the poet contemplates and it is analogous to the desire of an "unravished bride" or simply the desire to know "truth, beauty" and above all, how art, poetry, the urn (and/or life) can communicate that. I always thought that the poet concludes that art in general tries to represent life, but ends up creating a duality of desire in this kind of "representational art": the poet must know and art must sort of desire to be real, not frozen - in order to Truly represent life.
While truth and beauty, subject to opinion, can be immortal, they exist through these images (and life) and the concepts they conjure. So, running with "conjure," life conjures art which conjures truth and beauty, all of which is contemplated by life and the cycle continues.