Acts 3:19-21

It has been God's purpose since the foundation of the world to restore all things and for there to be a time of refreshing—we might say a breath of fresh air, breathing space, respite. The word that is translated as "restoration" here means "the establishment of something good following something bad," or it could also mean the establishment of what was predicted by the prophets.

Peter is stating that the respite and the restoration are the result or the consequence of something. The 'thats' are used in the sense of saying that one thing results in another. There is a direct connection between what precedes the 'that' and what follows the 'that.' The 'that' at the beginning is the action; the words that follow the 'that' are the consequence.

Now, if people repent—if they allow their minds to change and be converted—their repentance will play a part in the great events that are talked about in these two verses. He is saying, in effect, that repentance is the cause of respite, of restoration, and of the coming of Jesus Christ.