More precisely: suppose that all voters provide an ordered list of preferences, each complete and transitive (option A preferred to B, both preferred to C - no other options available): there does not exist a function that returns a "collective" preference so that ("non-dictatorship") there is no individual list that will always predominate irregardless of the other lists, and ("unanimity") if all voters declare the same highest preference the collective preference will reflect that, and ("non-irrelevance") the collective preference between two alternatives will only depend on the preferences voters claim about those two alternatives.

The page member rfreytag indicates, https://mises.org/wire/arrows-impossibility-theorem-exposes-... , has a very good explanation.

Edit: I realize there could be another (suggestive) way to express it: at least in the (theoretically possible) cases where preferences show a cyclic pattern (when similar numbers of voters claim A>B>C, C>A>B, B>C>A), there is no """optimal""" way to determine a collective preference.

Edit: there is again another nice way to express it - member ajennings shows it at the end of his video (see nearby) with a simulation: if when all voters express preference for an option the outcome reflects that ("unanimity"), and we take a decision in the controversial scenarios, and we demand that the collective preference between two alternatives will be a function of the preferences individual voters claim about those two alternatives ("relevance"), then one ordered list of preferences will make the others uninfluent ("dictatorship").