I'll have a go, join the crowd, that sort of thing!
Say you have an airfield at 1000' above sea level, and someone has drilled one of Hug Monster's holes down to sea level. If you lower an altimeter down the hole to sea level, and wind the sub-scale so that is reads zero, the pressure the altimeter will display is QFF. QFF is actual sea level pressure - this is the pressure shown on mean sea level pressure charts.
Now if you raise that altimeter up the hole to the airfield, and say the day is a hot one, it will not read 1000'. As the temperature of the air in the hole is higher than standard, it is less dense. As it is less dense, the rate of pressure drop with altitude is lower than the altimeter expects - so the altimeter will show an altitude lower than 1000'. Lets say it is a 23°C day (i.e. ISA + 10°) at the airfield. The altimeter will show 960' , once you have raised it up the hole.
Now, as a pilot, you know the actual height of the airfield from your charts/map, and you want the altimeter to show you how far you are above that actual elevation - so this pressure setting (with its 40' error today) isn't much use to you.
If you take the altimeter (sitting at the airfield) and wind it to show 1000' - the height of the airfield - then the pressure shown will now be the QNH. Much more useful, as now when you descend to the field, the atimeter will wind down to the airfield height as you touch down.
If you then take your altimeter (sitting at the airfield), and wind it so that it shows a zero altitude, the pressure shown will be QFE.
How it works - the tower/met observer measures QFE directly (or makes a minor correction from his instrument to the airfield datum). Then correcting for a standard atmosphere below the airfield, they calculate QNH - which they pass to pilots. Then they correct for temperature to find QFF - which they pass to the met people.