The first definition is the most usual one. Jumper is a very common word to describe clothing in British English, and is pretty well a synonym of sweater or pullover. It's made out of wool or similar material, stretches from your neck to your waist, and usually has long sleeves. You put it on over your head (or in other words, it doesn't open up the front - that's what we'd call a cardigan).
I believe that the second definition is an American one, but fairly unusual. This would be more commonly described as a pinafore or pinafore dress.