In the story Kew Gardens nature is given human characteristics and the people in the story are given animal and other natural characteristics. The snail is significant because it represents or mirrors man. The snail's journey (with a leaf obstructing his travel) represents or mirrors man's struggles through life.
Witness the struggle of the snail (perhaps finest passage in the story):
The snail had now considered every possible method of reaching his goal without going round the dead leaf or climbing over it. Let alone the effort needed for climbing a leaf, he was doubtful whether the thin texture which vibrated with such an alarming crackle when touched even by the tip of his horns would bear his weight; and this determined him finally to creep beneath it, for there was a point where the leaf curved high enough from the ground to admit him.
"The irony here is that the snail's journey mirrors man's struggles. Furthermore, from our knowledge of science, we know the load-bearing leaf is a non-issue; thus, much of the snail's struggle is rendered pointless. Is the omniscient God/narrator able to see, where we do not, the fruitlessness of our own struggles?"http://litkitten.blogspot.com/2006/10/few-on-kew-virginia-woolfs-kew-gardens.html
The story illustrates the interrelation of man and nature through many characters including the snail. The lowly snail is my favorite character and its struggles are a very powerful part of the story.