What bird is it whose tail spreads out like a fan?

Many birds can fan their tails, so it depends on what you mean by "large". It also depends what you mean by "tail" - most birds that appear to fan their tails, do not - they need functional tail feathers for controlled flight so generally cannot afford to have extravagant tail feathers. Unless you include domesticated turkey stags/toms, which fan their tails during courtship, the commonest and best known is the male peafowl - the peacock. Nearly as large are male Argus pheasants, which have far larger tails than peafowl. Only the turkey uses his real tail feathers.