"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.

The line you’ve quoted in your question is only a portion of a thought; it would help to consider it in full: “I love thee with a love I seemed to lose / With my lost saints.” The line is in keeping with the rest of the sonnet, which expounds upon the full extent of the speaker’s love for the object of the poem. In the lines immediately preceding the one in question, the speaker states, “I love thee with the passion put to use . . . with my childhood’s faith.” The speaker’s childhood faith is pure, wholesome, and total, and it is this intense, innocent love that the speaker feels. The simple, honest passion that characterized her religious faith is the same that characterized her love for the saints as a child.  The speaker assumed this saintly love to have been lost over the years as her innocence dissolved into maturity, but this feeling has been rekindled by the object of her desire. And so she loves him with this same wholesome love that she felt for the saints when she was a child, enamored with the stories of her faith.