In brief: Art has the power to communicate the truth of human experience.
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
Thus a connection is implied that the urn, an example of beauty/art, is uniquely capable of expressing the "flowery tale" of human life.
As to who "speaks" the line about beauty, Keats seems to be offering a voice to the urn at this point. The poet "speaks" the line but does so in a way that he is standing in for the urn and uttering the message that he feels the urn has to offer man.
Thou shalt remain, in midst of other woe
Than ours, a friend to man, to whom thou say'st...