When Shakespeare's sad and woeful narrator, after recounting all his sorrows, thinks of his beloved, his mood changes to happiness. He likens this change of mood (this "state") to the beautiful song of the lark.
The lark is a bird associated with morning and daybreak. Shakespeare compares its song to "hymns at heaven’s gate." In other words, the poem's speaker feels a holy joy fill his heart that reminds him of the lark's lovely song as he remembers the one he loves.
The lark is a symbol of a new day and new joy in this poem. It symbolizes the speaker coming out of the "night" of darkness and despair into the "morning light" of remembering that his happiness over his relationship with his beloved outweighs any sorrow he feels. He states in the final couplet that
For thy sweet love remembered such wealth brings
That then I scorn to change my state with kings.