Buck and Boost drivers for LED
There are two ways that a LED driver can supply more current than it draws from its power source.

1) If the source is at a higher voltage than the load needs, a "buck converter" can translate high voltage, low current to a higher current at a lower voltage. The product (voltage * current) is the same on input and output (minus some losses in the converter) So a 3 cell LiPo (11.4V) supplying 1 amp could be translated into 3 Amps into a white LED (about 3.2 to 3.5V)

2) You can draw a continuous current from the source, store it (e.g. in a large capacitor), and release it as a short burst of high current. A bright flashing light can be more visible than a steady light while consuming less average power.