What does it mean that believers are the epistle of Christ written on the heart?
Believers are living epistles of Christ because their changed lives visibly testify to the Holy Spirit's work. This work is written on the heart, not with ink or on tables of stone, so it is known and read by all men. The epistle is Christ's message ministered through human instruments.
In the context, Paul is defending his apostleship, reminding the Corinthians that the ascended Christ, not Peter and the eleven, sent him to the Gentiles. The Corinthians themselves, having turned from idols to the living God and come out of paganism, immorality, and idolatrous practices, were evidence of his ministry. Les teaches that their changed lives made them an epistle written in Paul's heart and known and read of all men. He applies the same idea to those saved through simple teaching: they become living epistles. The text says this epistle of Christ is not written with ink but by the Holy Spirit of the living God, not on tables of stone but on the heart. That is where it must be. Les also stresses that Paul's sufficiency was of God, not his education or Pharisee credentials, so the work is God's, not human.