How are birches described in the poem? What can they signify?

The birches signify the speaker's love of life, earth, and nature.
The speaker describes the birches using imagery that is both beautiful and melancholy. He describes how the sun's warmth melts hard shell of ice around the birch trees, so that the ice cracks and falls in a thousand crystals:

Such heaps of broken glass to sweep awayYou'd think the inner dome of heaven had fallen

Likening the ice to "the inner dome of heaven" is a lovely image that expresses the speaker's desire to find heaven back on earth.

The speaker also explains how the birches can become bowed by the ice, saying they are


Like girls on hands and knees that throw their hairBefore them over their heads to dry in the sun.

This is another lovely image.

The birches bring back to the speaker memories of childhood. He happily remembers (somewhat problematically, given that the trees have been likened to females) how he "subdued" and would "conquer" the trees by riding on them.

Finally, with melancholy, he says that he longs sometimes to start life over by climbing a birch tree toward heaven and coming back to earth again:


I'd like to go [die] by climbing a birch tree,
And climb black branches up a snow-white trunk

Toward heaven, till the tree could bear no more,
But dipped its top and set me down again.

The speaker longs not for heaven but for a chance to live life again, and hr dreams of the birch tree, which represents what he loves about earth, offering him that possibility.