Overviews, or pyramids, and resampling are all about making raster layers load faster when zooming and panning in your map canvas, by reducing the amount of data loaded when not zoomed in all the way.
You will need a large raster image.
elev_lid792_1m.tif will work fine for this example.
Generating pyramids essentially makes copies of your original data resized for different zoom levels. As you zoom out, the original data is resampled to fit the size of the screen. The pyramids do the same thing, but they let you decide what resampling method to use and generate this overview ahead of time. By generating them ahead of time, QGIS can load the image faster when you change zoom levels.
Resampling is a fancy way of saying that at each zoom level that is now 1 pixel is more than 1 pixel from the original data, so they need to be averaged in some way and the result assigned to the 1 pixel that is now available. Each of the different methods uses a different math formula to decide the new value and how much to smooth that value with neighboring pixels (so that it looks aesthetically pleasing). This is the same concept as when you shrink pictures so that you can e-mail them to your friends.
If you chose to save them externally, your overviews are stored in elev_lid792_1m.tif.ovr. Some other programs store the same thing in the .aux files; however, pyramid formats are not universally compatible between GIS applications.
gdaladdo command; refer to http://gdal.org/gdaladdo.html