This is a simple but profound teaching.
Regardless of what the reward is that He's speaking of it's obvious that living a life for the admiration and praise of our neighbors, co-workers, church members, friends, family etc. is of no value in the larger scope of Kingdom life.
Our 'acts of righteousness' or practical godliness or functional Christ-likeness - these spiritual disciplines are acted upon solely for His glory. It's impossible to be hypocritically righteous (continue reading the passage), or insincerely authentic.
To clarify, the goal isn't to keep our Christ-like actions hidden, unseen from others. But that their seeing isn't our intention.
Whom are you seeking honor from? Be-aware of your hearts intention.
Read Matthew 6:1-18 for the greater context.