The gap is the demand-side pressure term in the phillips-curve and in the taylor-rule. A positive gap is supposed to push inflation up and a negative gap to push it down, though the empirical relationship has been weak for decades.
Its fatal flaw is measurement. potential-gdp is unobservable and estimated with filters that are heavily revised, so real-time output gap estimates have been wrong by several percentage points at exactly the moments they mattered most.
Example: actual output is $29.3 trillion and potential is estimated at $29.0 trillion, a gap of plus 1.0%. Two years of revisions later, potential is restated at $29.4 trillion, so the gap was actually minus 0.3% and policy was tightened into slack.
Related: potential-gdp, phillips-curve, taylor-rule, nairu, capacity-utilisation