That’s a new term I learned from Dr. David Powlison after watching the video below.  Atmospheric repentance is based on the initial cry of the Reformation as articulated by Martin Luther in the first of his 95 Thesis:

When our Lord and Master, Jesus Christ, said “Repent”, He called for the entire life of believers to be one of repentance.

The point is that the expectation of every follower of Christ is to experience Godward change and transformation that begins with the heart.  The means by which we become more and more like Christ is through repentance and faith as the gospel mode of operation.  Christians are commonly called “believers” because of faith in Jesus Christ.  Christians should also commonly be called “repenters” because we are daily turning from sin and self-reign to glad submission to the reign and rule of Christ as King.  Our response to Christ is simultaneously a repenting faith or believing repentance, and when that characterizes the predisposition of a follower of Christ, it is atmospheric.