People or animals that jump, or (in British English) pullover sweaters worn over other clothing.
From jump + -er (one who does the action). The garment meaning originated in the 1800s from 'jump' (a short coat worn by sailors), which came from French 'jupe' (skirt). The animal/person meaning is straightforward.
The word has a delightful split personality — in America it means animals that leap, but in Britain it means a cozy pullover. This happened because 'jump' referred to a sailor's short jacket, which became the jumper we know today, while Americans never adopted the garment name and use the word for jumpers instead.
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