The difference is that "three times as expensive as" is specific, while "more expensive than" is not specific.
If John is 30 and his son is 15, then
John is twice as old as his son. = John �s age is two times his son �s age.
So, you can see that I am taking the expression "as old as" (which means equal to) and multiplying it by two, producing "twice as old as". This is a very common construction.
Now, with that said, here in the US, people are incorrectly using the same expression the other way, and saying "John �s son is twice as young as John". This doesn �t work. It is especially used when talking about prices, saying that one thing is three times cheaper than the other (trying to mean that the second item �s price is three times as much as the first). This doesn �t work, because "one time cheaper" would be "100% lower price", making its price zero. Then "three times cheaper" would have to mean "300% lower price", meaning that they would pay you twice the price to take it from them. I would be happy to buy things that way (where the seller pays me to take it), but I don �t think it �s going to happen, even if people say their item is "three times cheaper".
I hope this hasn �t confused you too much. If so, just ignore the long paragraph.
Bruce