The Chitting of seed potatoes is not a necessary task to grow potatoes, but it is a simple one that'll make growing your own far easier.
In order to chit all you need to do is to put your seed potatoes in to a light, frost free position until small green shoots appear from the eyes on the potato. You want dark stubby shoots, not the long breakable ones that form on potatoes kept in the dark.
This means they will sprout and grow more quickly when planted (usually about two weeks faster compared to un-chitted potatoes.) This means you can put off planting and avoid frosts.
An egg box and a window sill are the perfect pieces of equipment for this purpose.
Here's a little bit of information on seed potatoes and what they are. It also talks about different types of potato crops.
Monty Don helps to define seed potatoes on this video on the Gardeners' World website here.