As you would expect most grass grows vertically on a lawn, but if you get down and look more closely then you will see that a layer of weed and thatch builds up over time and sits along the top of the soil. This ultimately starves the grass of light and can lead to moss and other issues on a lawn.
Unlike a convertional rotary mower that just slices the top off each blade of grass Scarifiers have vertically acting blades that remove this thatch growing along the surface. As a result more light can get into the grass, drainage is better and the lawn will be healthier.
Early autumn is the best time for a deep penetrating scarification and thorough clear out of moss and thatch. If you are carrying out any scarifying in the spring it is best to wait until the hardest frosts have passed to that the grass roots have time to recover sufficiently. Springtime and through the Summer - if conditions allow - is best for light to moderate scarification/grooming. Many of the domestic market smaller machines have two seperate cassettes (pioneered largey by Alko) so that you can carry out a deep Scarification in the Autumn and more gentle work in the Spring and Summer with the raker style tynes.
Scarifying is only part of your general lawn maintenance, and you will need to fertilise and weed as well to make the most of your lawn.
One final point to bear in mind is that the condition of lawns will be adversley effect by mowing with blunt blades and cutting the grass too short! Raise your cut to 30mm plus as a minimum and the general lawn condition will improve whilst still showing a clean cut finish.