What is Sonnet XXIV by Elizabeth Barrett Browning talking about? What is the conceit in the poem? What are the problems and solutions? What poetic devices are in this poem?
What an odd rhyme scheme: ABBA ABBA CXXXCX. This was unusual in the mid-19th century, particularly for a poet of Browning's calibre.
Anyhow...She's talking about shutting out the pains and worries of the world and living as well as she and her lover can for as long as life lasts. She wants to cut the "worldlings" out of their sphere; worldlings are those who are concerned about material things, and such greed brings pain and does not bring pleasure. She wants to live as freely from such things as she can, like the lilies on the hill, nourished by the dews from heaven (a simple metaphor for the grace of God).
A conceit is an extended metaphor in poetry. In this case, the conceit is of a folding knife (a pocket knife), and it's compared to the "world's sharpness"--unpleasant things in life. In her view, those things can be folded and put away so they can't hurt them, where they won't feel the stab of greed.
The problem is that they are surrounded by people who are concerned with material things--almost as though they lived in America today, if you think about it--and she realizes that this way lies madness, or at least unhappiness. There is only happiness in love and warm and appreciation of what you already have, so the solution is to learn to do that. Their lives are to be "lilies" whose blossoms are white and healthy because the "heavenly dews" keep the roots moist; they live in nature, unassisted or hurt by man--associated here with greed and destruction. She understands that they have what they have because God gave it to them, and they should be grateful; in time, God will take it away, as well.
The poetic devices are the conceit mentioned earlier, but it comes in the form of a simile "the world's sharpness, like a clasping knife." Love is here personified, able to hold the closed knife. There's metaphor, also, in how she feels safe "against the stab of worldlings." This is part of her conceit; it doesn't refer to her literal fear that an evil man will stab her. There's more metaphor in her reference to "the lilies of our lives."