Originally, a "puddle-jumper" was a derogatory nickname for an automobile which was cheap, small, old, run-down, or some combination thereof. In other words, a flivver.
By extension, this term soon came to be applied to aircraft as well, usually small or old planes which seemed like they could barely get off the ground and could only take you somewhere very close by. This meaning is by far the most common usage for this term today.
"Puddle Jumper" is also a brand name for a maker of children's shoes, and especially the company's signature water-proof polka dot shoes for girls, as well as the brand name for a line of kids' personal flotation devices produced by lifejacket manufacturer Stearns.
Lastly, in the science fiction universe of Stargate "puddle jumper" is the nickname given to gateships. The name "puddle jumper" is a visual pun on the ships' ability to travel through the event horizon of a stargate, which closely resembles a pool of water, but the name obviously also has resonance with the nickname as given to earth-bound aircraft as well.