This definition comes from the technical glossary.
A hash below a target value which can only be obtained, on average, by performing a certain amount of brute force work—therefore demonstrating proof of work.
Proof of work
Proof of work — Bitcoin.org Developer Guide
Proof of work — Bitcoin Wiki
Bitcoin.org is community supported: 3FkenCiXpSLqD8L79intRNXUgjRoH9sjXa