it is a great system. basically he was a mathematician who was drawn into war (or something like that), and to stop himself getting bored, he found patterns of numbers in his head that makes calculating things easier. he was just trying to do calculations in his head, and over time realised easier ways to do some of them. then he recorded them in a book.
dont teach young kids this, you really need to know the normal way of doing things first. however, older kids at, say, higher sets in year 10 of high school would be able to cope well with this.
it is good, but really its more of a novelty now than anything else. you rarely need to calculate 19*119 in normal life, and if you do for whatever reason within your job, you'll probably have a calculator with you that can do it just as fast. and for _real_ calculations in physics or maths you'll need a powerful computer. it's still interesting though, and something you can wow your friends with.
another thing to look out for: Vedic mathematics. similar thing, but much deeper. not just a tool for doing certain calculations in your head quickly, but an entirely different way of looking at maths. what we're used to is a very standard approach, but not really the only one. some thing Vedic mathematics could hold the key to solving problems in maths we presently can't solve with our current way of mathematical thinking.