Like Tom himself, Goldberry is a mysterious being whose place in Tolkien's mythology isn't easy to establish. She seems to be some kind of river-spirit, though some have conjectured that both Tom and Goldberry belong to the order of the Maiar. For more on these possibilities, consult the entry for Tom Bombadil.
In literary terms, Tolkien seems to have intended her character to perform a symbolic role. In his Letters, he writes 'We are ... in real river-lands in autumn. Goldberry represents the actual seasonal changes in such lands' (The Letters of J.R.R. Tolkien, No 210, dated 1958). We can see this symbolism in Frodo's greeting, quoted above, which goes on 'O spring-time and summer-time, and spring again after!'
It has been suggested that Goldberry might in fact be an Elf, based on a passage in The Fellowship of the Ring (I 7, In the House of Tom Bombadil) where Goldberry is compared to a '...a fair young elf-queen clad in living flowers'. In their full context, however, these comments merely represent the awkwardness of the Hobbits on encountering her for the first time, as if they were visitors who had unexpectedly come across an elf-queen in a country cottage. This doesn't necessarily imply that Goldberry herself was an Elf (and Tolkien's comments elsewhere make it fairly clear that he didn't consider her to be one).