The subject is taken from the narrative poem 'Aurora Leigh' (1856) by Elizabeth Barret Browning. Aurora, an orphan raised by her aunt, aspires to be a poetess. On the morning of her twentieth birthday she rejects a marriage proposal by her cousin Romney Leigh. She chooses to devote herself to her vocation in defiance of Romney, who disparages her verses and wants her to dedicate herself to his philanthropic causes. Aurora tells Romney that what he loves 'Is not a woman, Romney, but a cause: | You want a helpmate, not a mistress, sir. | A wife to help your ends, - in her no end!'
The painting depicts the moment when Romney has been refused and is about to take his leave. Aurora holds a book of her verses which Romney has found in the garden and made fun of.
http://www.tate.org.uk/art/artworks/hughes-aurora-leighs-dismissal-of-romney-the-tryst-n05245/text-summary