Rain, in "Wash away," works like a reset button for the mind. The speaker describes feeling afraid and weighed down by mistakes, and says that whenever rain arrives, those feelings are carried off with it. The "storm / That is in my brain" is a nice twist: the real weather outside becomes a way of talking about the turmoil inside, and the gentle rain is what calms it.
The feeling here is hopeful rather than heavy. The speaker admits to fear and to making mistakes, but the poem doesn't dwell on them. Instead it moves toward relief and a fresh start. By the last stanza, the "new day" brings a "new" brain, with the quotation marks around "new" hinting that the speaker may know this renewal is partly a feeling, not a permanent change. The short lines and simple repeated words make the mood quiet and soothing, a bit like the steady patter of rain itself.