Radiance is the currency in the 3DS version of Skylanders: Spyro's Adventure. It comes in both vials and chests and is used to pay for Magic Items and can also grant Victory Points (experience) to the Skylander when a level is completed. In some levels, collecting a certain amount of radiance vials is the objective for getting a Radiance Crystal.
In Skylanders: Lost Islands, Radiance is a source of energy used by Skylanders during adventures. It's obtained by harvesting plants in great quantities, and is stored in bottles. It is unknown if the Radiance is exported from the Radiant Isles or it's also found in the Lost Islands.
Collecting 10 Radiance rapidly will give you a Radiance Rush, which doubles the amount of Radiance obtained. When you have a Radiance Rush, all Radiance will change colors from white to red. A Radiance Rush only lasts for a limited amount of time.