A one-way function is a computation that is very easy to perform but very difficult to reverse. Hashes are the most prominent example of one-way functions as they pertain to cryptocurrency. Depending upon the nature of the function involved, the process via which it is implemented, and the hardware involved, running a one-way function can take as little as a fraction of a second to compute and as long as the heat death of the universe to reverse.
Two factors help intuit the practical irreversibility of hash functions: the variable size of the input leading to a fixed size output (frequently data from inputs significantly larger than outputs is discarded) and repeated 'modulo' operations. The latter essentially entails dividing a number by another and outputing the remainder—this is very easy to do one way and significantly harder to do the other.