A sweater is a relatively heavy garment intended to cover the torso and arms of the human body (though in some cases sweaters are made for dogs and occasionally other animals) and typically supposed to go over a shirt, blouse, t-shirt or other top. Sweaters tend to be, and in earlier times always were, made from wool (typically of sheep though possibly of alpaca or other type), though they can be made of cotton, artificial fabrics or some combination thereof.
A hockey sweater was, in the early days of ice hockey, recognisable as what we would now call a sweater, but has evolved into a sort of jersey.
In British English a sweater is called a jumper. A related garment, a jumper with an open front fastened by buttons or a zip, is called a cardigan.