Looks like Hydrangea macrophylla..common name mophead Hydrangea.
Sadly the leaves are not looking as green and healthy as I would expect.
The colours of the flowers can change depending on your soil.
Advice re pruning from RHS.
"Dead blooms on mophead hydrangeas can, in mild areas, be removed just after flowering, but it is best to leave them on the plant over winter to provide some frost protection for the tender growth buds below. Remove the dead flowerheads in early spring, cutting back the stem to the first strong, healthy pair of buds down from the faded bloom"
