Displacements (disp0-#.dat) are black and white textures for your map. Don’t try to put the main colour palette on it, as you will see weird things. Click on the Edit-Use Grayscale Palette instead. Displacement is a way to add a texture to your map, for example to make it grassy, or snowy, or whatever your Landscape Palette is.

Displacements tell Populous where it should start using the higher places earlier (darker parts), and lighter parts later. If you use it correctly, you can create a nice texture for the terrain, but if you put some weird images as displacements, the game will use the wrong colours. The most effective kind of displacement is where the corner of the land and the water is. If you use the wrong displacement, water colours will appear on the lowest parts of the land. You can correct those with the Landscape Palette to give lesser or more space for the water colours, but giving too much will make the landscape look blue (or whatever colour your water is) also it may give weird square looking edges at the corner of water and land.

Here are two screenshots of two different displacements used on the same terrain style: