I am sure you will get different opinions here....but here is mine for what it is worth.
A tippet is naturally the bit of line you attach your fly too. Too thick and the fly does not behave naturally, too thin and you can crack the fly off on the cast or a fish can break you on the take.
Very generally, a small fly requires a light tippet, a big fly a heavier tippet. For example, a size 16 buzzer would fish better and look more natural on a 4lb tippet but a size 6 weighted Cats Whisker would be better on an 8 lb tippet.
Normally the "leader" tapers from the end of the fly line to the fly. This aids fly turnover. Many people use a tapered Polyleader for this rather than the older style knotted leaders that perhaps started with 2 feet of 15lb line, then 2 feet of 12, 2 feet of 10, 2 feet of 8 and then onto a tippet of 8 or 6lb line.
The tippet also serves to push the fly away from the fly line in that if you attached 5 feet of 4lb line to your exisiting 8lb line, your fly is a further 5 feet away from the tip of the fly line..and so in very clear water, less likely to scare a fish.