Compaction is when the soil beneath an area of your lawn is squashed. The lack of air spaces between soil particles means that water runs off it and starves the lawn. Fine grasses will quickly die off, and moss soon sets in.
Compaction can be caused by turning the mower around on the same spot every time, or by people walking across the same stretch of grass repeatedly. It can be solved by regularly spiking the area with a lawn spiker and watering it. If you do not have a spiker, aerate the soil well with a fork inserted right to the shoulder every 15cm. Your objective is to break up the underlying soil so there are more air spaces to hold water near the roots and to prevent the rain from draining off.
If the build-up of thatch gets to more than ½ inch deep, it will start to reduce the ability of fertiliser and water to reach the grass roots. This makes grass growth slower and also provides good conditions for moss. A certain amount of thatch is desirable to make your lawn hard wearing but if it stops water from getting through to the roots you have a problem.
Spiking is the recommended way to get rid of unwanted thatch. This can be done using your garden fork if you do not have access to a dedicated spiking machine. Insert the fork into the soil to its shoulder, wriggle it around and withdraw it. Repeat every 15cm or so across the entire area that is affected. This action loosens the soil beneath the lawn, creating air spaces around the roots, so you can feed and water it more effectively.
If moss has already set in, then it must be treated. First, treat the area with BS Feed, Weed and Mosskiller which will protect the area for up to eight weeks. Then, after a couple of weeks, remove as much of the moss as possible from the area by raking. For small areas, a sprung wire or fan rake will suffice, but a lawn scarifier will make it easier and you will find one invaluable for a larger lawn.
Once the area is cleared, it will most likely need to be overseeded with grass seed. If the grass is thinning then a patch repair mixture such as BS Renovator - Lawn Repair Grass Seed will usually suffice. Otherwise, you will need to reseed the area with a grass seed mixture that matches the rest of the lawn as closely as possible.