The previous post did a nice job with the analysis of the poem.  I would like to add that the use of the lines might be a desire to externalize an internal experience.  The drive of the poem is to convey an emotional sensation of love in external terms.  The invocation of a political end might be one way to do this.  In comparing the love of another to the love of justice and its pursuit, the speaker makes the claim that an external experience to which there can be open relation to a political experience.  Barrett Browning was insightful enough to understand that the pursuit for justice and quest for what was right in a political sense is something that can animate individuals to believe, galvanizing them into action.  At the same time, to be able to relate this public quest to a private experience can help allow a sense of understanding to emerge.

This whole poem is a list of all the different ways the speaker loves the person the poem addresses.  Elizabeth Browning was writing this to her true love, Robert Browning.  In these two lines she is expressing the pureness of her love for him.  When she states that she loves him freely, she means no one else is 'making her' love him.  She loves him because it is what her heart is telling her to do.  She compares that feeling to the feeling of men who do the right thing just because it is the right thing to do.  The next line follows up that idea.  She says, "I love thee purely as they turn from praise" meaning I love you genuinely for the sake of love, not because I will be praised for it.  Just as good men don't do the right thing for praise, they do it because it is the right thing to do.  These two lines work together to compare her love to the actions and attitudes of good men.