Leaders and Tippets

I have a question: What is the general purpose of having a leader and a tippet for fly fishing? I know what they are, just don't understand the purpose of it. I understand that for trout fishing, the tapered tippet allows for a much more stealthy presentation. But when it comes to other more generalized scenarios, what advantage do you gain by using the leader/tippet combo as opposed to a single longer piece of monofilament as the leader with the fly tied on to that?

Funny you asked this question only days before I asked Tom for help in tying my leader to my fly line and he provided us with the answer. I wondered the same if a single size piece of mono or fluorocarbon would provide the same effects as a tapered tippet. Also I wonder / worry about the strength of using a tapered tippet since the end of it is such a small strength of line. I know using an 8'+ rod with pretty stretchy line the force on the line is probably very minimal. Causes me some real issues with setting a hook into the hard mouth of a large bass. I should probably google some of this stuff.