Public or outward acknowledgement is the reward that Christians who are secretly faithful receive from God.
One way or another, our private devotion to God will show outwardly. We don't have to try, we don't have to uplift ourselves to others, we don't have to beg people to believe that we know God through Jesus Christ.
When we are faithful in seeking God's face and drawing nigh to him, his power will emanate from us. When we pray, fast and give from our secret closet, God will reward us outwardly.
We will receive some type of open acknowledgement, from God, for our secret faithfulness.
Matthew 6:6
Matthew 6:17-18
Matthew 6:3-4