The distance mask is a very useful stamper feature to fade in or fade out the influence of a stamper from the center of the stamper towards the edges via a curve. To use it, simply adjust the distance mask curve and keep in mind that the left side of the curve represents the center of the stamper, while the right hand side represents the outer edges of the stamper. This might sound confusing at first, but if you look at the example below it quickly should become clearer.
Note that you can't see the influence on the mask immediately on the stamper preview, but it should be applied in the result of the stamping process. Another common issue is that users forget to disable the stamper preview after stamping and the preview mixes in with the actual terrain, hiding the actual stamping result.

If this does not help, can you please try to follow these steps in an empty scene: 

1. Open Window > Procedural Worlds > Gaia > Gaia Manager and click on the "Create Terrain & Show Stamper" button 

2. Select the stamper and select the "Andes Mountains" stamp. Click on the distance mask and adjust it to look like in the screenshot below. You can get the exact same curve as in the screenshot by right clicking on the right node in the curve, select "Edit value" and then set the value to 0.

3. Check the Stamper Preview (Enable with the Preview button if not there) It should look something like the stamper in the screenshot below, maybe in different color but that is ok.

4. Click "Stamp" in the stamper, then disable the stamper preview with the preview button.

5. Your end result should look something like the screenshot below. Note how the influence of the stamper was faded out towards the borders of the terrain according to the distance mask you created.

By pressing the "Undo"-button, adjusting the distance mask curve and hitting stamp again you can test the influence of the curve on the stamper.
This screenshot shows a reversed distance curve that creates a lake in the center of the terrain:

This example shows a ring like terrain structure due to a wave pattern in the distance curve: