I have never really understood this and the documentation doesn´t explain it.
Say you have some DEM data, a raster where each pixel represents the elevation of that pixel.
You load it into ArcMap, and it would generally default to a gray scale image (black to white colour ramp).
If you want to send someone a "picture" if the data, rather than the data itself, you can apply another colour ramp (maybe Elevation 2 or something), maybe use a graphic to cut out a small section, if you right click on the dem and select data / export, then click the Use renderer & force RGB, the exported raster is now a 3 band (RGB) image of the original.
Original gray scale raster.
New colour ramp.
RGB image output.