Paul begins chapter 3 by saying that he was unwilling write letters approving himself as an apostle, but he encourages the Corinthian believers to consider the evidence of the Spirit at work in his ministry among them (2 Corinthians 3:1-3). Not that Paul took any personal credit for this, but he acknowledged that it was God who had gifted him (2 Corinthians 3:4-5).
Paul then contrasts the Old & the New Testaments - the new as life giving and more glorious than the Old which though glorious could only produce death (2 Corinthians 3:5-11). The New was contained in the Old in types and shadows, but natural Israel because of their unbelief failed to look beyond the Old to that which God had purposed in the new (2 Corinthians 3:11-15). But when the heart turns to the Lord, the veil is removed and the glory of the new is able to be seen (2 Corinthians 3:16). It is this change of the heart that then opens the way for the revelation of Christ to the inner man, a progressive revelation of His person that changes us from glory to glory by the work of His Spirit (2 Corinthians 3:17-18).