Mariana is based on Measure for Measure by Shakespeare. I don't recall the plot, but it involves a girl called Mariana (a side character I think) who was jilted by her fiance after her dowry was lost in the sea. Tennyson writes from her perspective. She bemoans the fact that he will not come.
You can find the rest here.
Mariana by John Everett Millais
WITH blackest moss the flower-plots Were thickly crusted, one and all: The rusted nails fell from the knots That held the pear to the gable-wall. The broken sheds look'd sad and strange: 5 Unlifted was the clinking latch; Weeded and worn the ancient thatch Upon the lonely moated grange. She only said, 'My life is dreary, He cometh not,' she said; 10 She said, 'I am aweary, aweary, I would that I were dead!'
As for the paintings, the poem inspired the Pre-Raphaelites, who were all about feeling and passion and sentiment. I don't know if you've noticed the lyrical ones with a story were those emulated by the Pre-Raphaelite Brotherhood?
Tennyson also wrote another poem called Mariana in the South.