The Displacement Map effect distorts a layer by displacing pixels horizontally and vertically based on the color values of pixels in the control layer specified by the Displacement Map Layer property. The type of distortion created by the Displacement Map effect can vary greatly, depending on the control layer and options you select.
This effect works with 8-bpc, 16-bpc, and 32-bpc color.

The displacement is determined from the color values of the displacement map. The color values range from 0 to 255. Each value is converted into a scale ranging from -1 to 1. The displacement amount is calculated by multiplying the converted value by the maximum displacement amount you specify. A color value of 0 produces maximum negative displacement (–1 * maximum displacement). A color value of 255 produces maximum positive displacement. A color value of 128 produces no displacement.
The effect uses the control layer specified by Displacement Map Layer, without considering any effects or masks. If you want to use the control layer with its effects, precompose it. If the control layer isn’t the same size as the layer to which the effect is applied, it is centered, stretched, or tiled depending on the setting for Displacement Map Behavior.
Select Expand Output to allow the results of the effect to extend beyond the original boundaries of the layer to which it’s applied. Select Wrap Pixels Around to copy pixels displaced outside of the original layer boundaries to the opposite side of the layer; that is, pixels pushed off the right side appear on the left side, and so on.
Rick Gerard provides additional explanation and an example project for the Displacement Map effect on his website: www.adobe.com/go/learn_ae_rickdisplacementmap.
Eran Stern provides a video tutorial that shows how to use the Displacement Map effect with a text layer and some smoke footage to create a smoky text title sequence:
http://cowcast.creativecow.net/podcast/smoking-letters-in-ae-cs3--203
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