"Only connect" is doubtless the most famous line from this book, and typical of Forster's knack for sprinkling unexpectedly modern-sounding phrases into his prose.
This is the story of the Schlegel sisters: half German Edwardians living in London. They are intellectual and comfortably off, but more bohemian/Bloomsbury than establishment. They encounter the wealthier and more conservative Wilcoxes and the struggling clerk Leonard Bast. Their altruistic attempts at social engineering are sometimes amusing but ultimately tragic.
(Incidentally, "Howard's End" is the name of a house that has great significance in the story; it doesn't refer to the death of someone called Howard.)