The term “provably fair” is unique to the blockchain industry because of the implications regarding verification/validation that come with blockchain technology.
Provably fair is used in the context of gambling and casinos. Whenever a game is being played digitally how can the player be certain that the algorithm has not be stacked against him in such a way that will never allow him to win? When in dealing with blockchain environments; if a gambling game is deployed as a DAPP, then the machinations that underlie its operations can be verified.
Flip of a coin.
In theory, if a coin is flipped 100 times, the amount of times there would be a heads & tails would average out to 50:50 (or a deviation close to that 47:53). If somebody is betting on the outcome of that coin flip they want to have guarantee that that coin has not been altered in a way that would favor their counter party; fair players want the circumstance to be neutral (sore losers need to cheat). If a coin is being flipped digitally, they must be some mathematic randomness that takes place and can be proven upon request; it must be “Provably Fair“.