The word "jumper" when used to mean a sweater comes from an obsolete term for a large, loose men's jacket called a jump. "Jumper" is a term mainly used in England, while the term "sweater" is more common in American usage.
In the 1800s, artists and workmen often wore a large thick shirt called a "jump" which would be called a smock in today's terms. It later became "jumper" when referring to any knitted or crocheted top in England, or "sweater" in the United States when it became regular winter wear for outdoor types, especially those playing sports. Their activity would cause them to sweat, hence the term "sweater."
The terminology can be confusing because a jumper is also a sleeveless dress worn over a shirt or a one-piece article of clothing for a small child in both British and American English. In the United States, this definition is what usually comes to mind. However, in England "jumper" first evokes images of what many Americans call a sweater.