It looks like Anemone coronaria de Can group, which has finely divided leaves and grows from a small tuber. They can be red, pink, blue/violet or white, and can have single or semi-double flowers, (i.e. petals in more than 1 layer, but not covering flower centre). There is a semi-double white variety called 'The Bride', which is beautiful. This year I have grown a single one which was nearly blue in colour and lovely. It has just finished flowering, having started in March, here where I live on the east coast of England, though we did have a mild winter and early spring. Later, the leaves will yellow and die back, but don't throw it away. It is a herbaceous perennial and will grow again. It likes full sun and well drained soil. If they are planted in the garden and your soil gets waterlogged or very cold in winter, they may not survive. You can either lift and dry the tubers after the leaves have died and store them to plant again for next year. (Soak dry tubers overnight in water before planting). Or, an easier option is to grow them in pots, as I do, as I have heavy clay soil which gets very wet in winter. I leave the pots outside over winter, but if you live in an area that has severe winters, you may need to put them somewhere sheltered. Hope this has helped.
