When you're making adjustments, the sliders default to a certain minimum increment, such as 10 or 1, depending on the adjustment. Oftentimes you might want to make a finer adjustment without having to resort to keyboard entry. Finer adjustments might be useful for straightening or white balance, for example.
Aperture provides "infinite sliders" to allow exactly that. When you put your mouse pointer over the numerical value of your adjustment, to the right of the slider, the pointer will convert to an I-beam, which indicates the availability of the infinite slider. To use it, press and hold the mouse button when the I-beam is visible, then move the mouse left and right to adjust.
To change the rate of adjustment, use the Shift and Option keys. Shift will accelerate the rate of adjustment, while Option will decelerate the rate of adjustment to the finest available increment.
Tip: For certain adjustments, infinite sliders can reach extremes of the adjustment range which are not available to the regular sliders.