In brief: Art has the power to communicate the truth of human experience. 

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The line in question is somewhat difficult to explicate, but when taken in context of the rest of the poem, Keats seems to be suggesting that the urn presents a set of messages. Taken together these messages can be identified as truth -- or the conclusive notions taken away from images of life that function as a comment on the nature of that life. 

One way to paraphrase the line "Beauty is truth, truth beauty" is to say that art conveys human knowledge and insights better than any other conveyance of meaning (better than science, perhaps, or better than music).

The urn, after all, is depicting human life in various stages and engaged in various tasks. Youth and joy and sacrifice and, thus, religion are all represented. Furthermore, these ideas are presented in such a way as to maintain their mystery and their enigmatic significance. None of the magic of these aspects of life is lost when represented on the urn.

A repeated suggestion in the poem is that by not speaking and by maintaining an allegiance with silence, the urn is capable of articulating both the substance of life and its more mysterious nature.

Thou still unravish'd bride of quietness,

       Thou foster-child of silence and slow time,

Sylvan historian, who canst thus express

       A flowery tale more sweetly than our rhyme

Opinions are divided whether this is Keats' or the urn's comment. Due to the punctuation of the lines, it is conceivable Keats is declaring that beauty is the only time that a subject's true inner nature truly revealed.

The urn speaks these lines to mankind. They address an age old philosophical question: what is truth? The lines mean that rather than seeking the answer to this question in pure reason, we should seek it in beauty: that beauty is the truest thing humanity can experience.

Critics through the ages have been troubled by these last two lines of this wonderful Ode, as they seem on the surface at least to have very little to do with the rest of the poem and the depiction on the scenes of this Grecian urn that Keats so powerfully visualises for the reader. However, it is clear through this statement that Keats is actually making quite a philosophical comment about truth and beauty. One way in which this statement can be interpreted is to consider that the scenes on the urn are true and beautiful because they are frozen in history and therefore separate from the messy reality of day to day living. Note how the final two lines are mentioned in a context that draws the reader's attention to the eternal nature of art contrasted with the ephemeral nature of human experience:

When old age shall this generation waste, Thou shalt remain, in midst of other woe 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 Grecian urn becomes a powerful symbol of permanence when compared with the mortal lives of humans, and Keats therefore uses this urn as a symbol of beauty because it is self-contained and frozen in time. By contrast, the lives and experiences of humans are never self-contained and constantly lack answers. The poem therefore points towards a divide between art and experience, and suggests that such truth and beauty can never be fully captured in real life. Humans are left to appreciate such flawless truth and beauty in the form of art alone.

I wonder if there are any other two lines that are debated so much.  The closing couplet to the poem is really profound.  There will be no easy answers here and I strongly advise you to take what you find here, what you find in your class discussions/ notes, your instructor's analysis, and, most importantly, your own perceptions and merge them together in understanding the last two lines.  I think that the context of the poem of Keats staring at this urn and the beauty within it is important.  The urn is the launching pad for the philosophical ideas and the inquiry that Keats explores in the poem.  The challenge here though is that Keats struggles to make the leap between what is happening in the urn and the world outside of it.  Art has the advantage of being cloistered in one moment in frozen time.  The beauty of the urn is suspended because it is within art.  As an artist, Keats was driven with the idea of how can art's perfection be something within the grasp of the real world.  Probably more than any other Romantic thinker, Keats was animated with a sense of this notion of artistic and aesthetic perfection in his work.  How does he, as an artist, create a realm that transcends frozen conditions and brings out the essence of truth and beauty?  How does one move from mere abstraction to actual replication of such elements?  His closing lines might be a way for him to attempt to make peace with the fact that elements of truth and beauty might lie beyond his grasp, beyond anyone's, and simply exist as a realm for us to wish to enter, where "angels dare to tread."  It is almost as if the last lines create a sweet pain of consciousness where we know that we will never be able to create such elements in our art, but rather to simply behold them and bask in their presence is enough.  When Keats sees the beauty and truth of the urn, it fills him with enough satisfaction to be able to appreciate and express that he can feel such an experience.  This subjective conception of supposedly objective ideals is consistent with Romantic tendencies.  At the same time, the closing lines help to bring out the "negative capability" that is such a part of Keats' work and Romanticism in its response to the Enlightenment period's affirmation of scientific inquiry.  The idea that there are realms where we, as human beings, must be content with the unknown is something that Romantics, and especially Keats, advocated, and the closing couplet to the poem might be a statement in this light, as well.

With the ode as a meditation upon the images of the Grecian urn, the final lines present a paradox. For the urn - the "ye" of Keats's apostrophe--beauty is truth as the "Fair youth," for instance, will always remain so; he does not exist beyond the unthinking state of nature.  "Truth is beauty" is so since there is no existence for art beyond the beauty.

However,--and here lies the contradiction-- for humans, beauty cannot be preserved and, therefore, be truth.  There is, instead, some existential despair here as beauty can only exist in an artificial state. Yet, if the reader goes beyond this remonstrance of Keats, he/she will that the final lines of Keats liberates man to be imperfect.  And, imperfection causes all human beings to make and remake art, one form dies and one lives with each rebirth of art, which is a common theme in Romantic poetry.

Interesting questions.  I have always assumed that the speaker looking at the urn was addressing the urn...that the truth is in the stories depicted on the side of the urn and that the beauty of these scenes has been captured there forever.  As long as the urn survives and is able to share its stories with the onlooker, the truth and beauty is there to be taken in and enjoyed.  If the urn is the speaker, then again, it is addressing humanity in that there is truth and beauty in life and some glimpses of it have been captured on the sides of the urn itself. This would translate to happiness and satisfaction in the joy--truth and beauty--that we experience daily.  It is all we need to know, if we can indeed slow down enough to recognize it when we see it.