oRughly:
- before them, cryptography was half an art, half hopeless, half a set of wishful thinking and recipes of the type "doing that should be OK" — and definitely blurry and fuzzy enough to have more than two halves;
- they essentially defined what cryptography should be, in terms of expectations (what should be expected from a good crypto system, wrt to a rigorous mathematical model and definition: two encrypted messages should be indistinguishable according to this definition, etc); pointed out that aiming at truly perfect encryption was hopeless (and provably impossible for real applications), and introduced the notion of computational indistinguishability ("it looks exactly the same with overwhelming probability, unless you have a supercomputer and three millenia ahead of you to crack it");
- and so on.
Roughly speaking, without their work, there wouldn't be (say) any of all the recent advances in cryptography, secure computation, and many more...