On the surface, this poem is about springtime. Rossetti discusses how different elements in nature possibly anticipate and get excited for the spring to come. She wonders if "the sap is stirring" in the trees, and if "wintry birds are dreaming of a mate". In the spring, birds find their mates, sap flows from the trees, and other things happen in nature, and Rossetti ponders whether they are anxious for that new life and those exciting events.
Then, she brings a comparison to her own life. She feels like she has lived in an eternal winter; she has been cold, frozen, left out, not experiencing the joys and beauties that life has to offer. So, she wonders if, finally, her "heart and spirit will find out their spring," and if she will finally feel nourished, beautiful, and experience new things. She hopes so; she hopes that it is not only that "the world alone will bud and sing" and not her own life.
She ends by saying that no matter what, in spring, a bird "will always find its mate" even if it is later than the other birds. So even if she hasn't experienced a metaphorical spring in her life, she has faith that someday she will be able to "blossom and rejoice and sing" at the wonderful events occuring in her life.
I hope that explanation breaks things down a bit for you. The main theme is having a life that is much anticipated and desired. It is waiting patiently for the good things in life. It is rejuvenation and rebirth, a second chance at life, and the hope that that brings.