An important development, an advance, a discovery, a leap forward. (dictionary meaning of breakthrough )

Holiness breakthrough happens when a person receives what the New Testament calls, a pure heart. Getting your personal holiness breakthrough comes down to understanding that Jesus dealt with the sin issue once and for all in His suffering, His death, and His resurrection. John the Baptist called Him "the Lamb of God who takes away the sin of the world." The Apostle Paul tells us, "He has appeared to put away sin by the sacrifice of Himself." (Jn 1:29) (Heb 9:26)

Having removed sin at great cost to Himself, Jesus cleared the way for each believer to have a pure heart.