"Sonnet 43" by Elizabeth Barrett Browning is one of the most famous love poems in the English language. Behind it is a historical love story. The poet wrote it to her husband, Robert Browning, who met her after feeling a passionate attraction to her poetry. Knowing that her father would disapprove, Robert courted and married Elizabeth in private, and afterward they moved to Italy. Elizabeth's father did disinherit her, but the couple lived a happy life together and even had a son.
As the first line indicates, Sonnet 43 is comprised of various ways Elisabeth expresses her love for Robert. In order to understand the meaning of the line expressed in the question above, you need to read the sentence in its entirety. It begins in line 11 and concludes in line 12. The sentence says in full, "I love thee with a love I seemed to lose with my lost saints." The "lost saints" that Elizabeth mentions are the people whom she used to love and cherish in her life but doesn't anymore. She has transferred all the love she used to direct at former loved ones to the lover she is addressing in the poem. She may also be referring to a piety she once felt for the saints of the Christian church. Even this transcendent love she now directs toward her husband.