After learning this poem for my class, I get stunned by its meaning all over again whenever I go back to that classroom.
Basically, the speaker is looking at the birches bending and he says he prefers to think that some boy had been swinging them, when in truth it was the doing of ice-storms--which he clearly knows. My favourite lines of the poem are "I'd like to get away from earth awhile / And then come back to it and begin over." The speaker wants to get away from reality by swinging on birches, but he also wants to return to earth and begin again.
Therefore, the act of swinging on birches is a metaphor for poetic imagination. Sometimes we get tired of getting on with everyday life. We want to get away from it because it's just so stressful. During such times, we experience the need of distancing ourselves from reality and seeing the world with imagination. But we can't do that forever; we have to come back to reality and get on with our hectic lives, just like how the tree sets us down on earth when it cannot bear our weight anymore. So the speaker is trying to say that we need to distance ourselves from reality for a while and see the sky with the eyes of imagination.
Isn't it genius? I'm currently writing a paper about this poem but I don't feel even an ounce of stress. Merely thinking about this poem heals me. Reading "Birches" itself is truly the magical experience of swinging on birches.