To be fair, most of the stuff that isn't pretty pictures goes past me. However, one thing he did do was completely eliminate the validity of the (Nobel-prize winning) Black-Scholes model.
So we have E. Fama (another Nobel prize winner) with his efficient market hypothesis, stating that in a perfectly rational market, prices are random. The loophole for economic theorists, and the basis for Black-Scholes, was that price variances were thought to be predictable. Prices were random, but their fluctuations were generally not, and could be modeled as a Gaussian distribution. Mandelbrot suggested that this a soothing inaccuracy: prices were capable of varying much more wildly than that. He suggested that a Pareto distribution was more accurate.
So then we have one of the more fundamental problems in Economics: it is not a science. It's more of a cult for math geeks, in my opinion. If you can't prove that markets follow a Pareto distribution (implying an unpredictably-random price volatility), then why should economists listen to you? Black-Scholes gives them partial results, and that's better than nothing, right?
B. Mandelbrot: The Misbehavior of Markets: A Fractal View of Financial Turbulence
"I'm not asking for anything exorbitant. I ask only for $1 per year more than the salary of anyone else here, as a token of recognition that I am a better mathematician than anyone else in the department."
D said that he would think it over.
During their next meeting, M asked D what he thought of his proposal. D replied that after the deepest consideration, he had decided against it.
"Why?" M wanted to know.
"Because the reason for paying you that additional dollar isn't true," D replied.