Hi Gadz,
not sure which bit you don't understand but here goes with my explanation.
When you fish boilies they can be quite difficult to hook up if just using a standard hook as they are quite hard and if you do manage to hook one they can obscure the point of the hook so you do not get a good hold on the fish, the fish can also "suck and blow" the boilie and hook out of their mouth when a boilie is just put on a bare hook.
A hair rig has an extra bit of line below the hook (as shown in Brians link) which can be used to attatch the bait to. This leaves the whole of the hook exposed and gives a better hook hold, the fish can spit out the bait but the hook remains attatched

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You can drill a hole in the boilie and slide it on to the extra bit of line and then put a little plastic boilie stop through the loop and gently pull the boilie back down onto the stop to stop the boilie falling of.
Other baits can be threaded on to the hair using a baiting needle, again using a small boilie stop (or piece of grass etc. ) to stop the bait pulling off.
Some hair rigs are tied with a small bait spike tied to the hair, this bait spike can be pushed into a hard boilie and is a bit quicker and easier to use than the loop and boilie stops which can be a bit fiddly.
When fishing paste you can use a hair rig that has a small spring tied to the loop instead of a spike and the paste can be moulded around the spring, again leaving the hook free for a better hook hold.
Hope this helps, if not just post again and someone will put you right
