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Its a little wisp of a circuit that allows you to drive a blue or white LED from a low voltage. Normally, if you want to light up a blue or white LED you need to provide it with 3 - 3.5 V, like from a 3 V lithium coin cell. But a 1.5 V battery like a AA cell simply will not work. But using the Joule Thief, it works like a charm. Not only does it work with a brand new battery, but it works until the battery is nearly dead-- down to 0.3 V. Thats well below the point where your other toys will tell you the battery is dead, so it can steal every last joule of energy from the battery (hence the name). To learn how to make one, watch the video, which is available in a variety of formats.

0.3 to 1.5V LED Flashlight Circuit Diagram