"You are the light of the world. A city on a hill cannot be hidden. Neither do people light a lamp and put it under a bowl. Instead they put it on its stand, and it gives light to everyone in the house. In the same way, let your light shine before men, that they may see your good deeds and praise your Father in heaven." (Matthew 5:14-16, NIV)Context: Matthew 5:1-16
Letting your light shine! Tell others about Jesus, right? This is important, but Jesus didn't mention speaking in Matthew 5:16. Jesus parallels "let your light shine before men" with "that they may see your good deeds." Jesus used the metaphor of shining our light to describe people seeing truth through our lifestyle.
Jesus described this lifestyle with the word kalos, translated "good" in "good deeds." He didn't use agathos, good in the sense of righteous or pure actions that show our righteousness. Kalos means appealing or beautiful, such as good food. Appealing works doesn't mean doing what the world wants, blending into the background and hiding one's light. It's God working out His purpose in our lives, so that others see Jesus in us. That will move people to praise God.
In the phrase "praise your Father in heaven," the word translated "praise" is doxazo. It's noun form, doxa, means glory or praise. Paul used it's primary meaning in Acts 22:11 when he described the brightness of the light that blinded him. Recognizing God's glory, the brilliance of His light, is an important element of praising God. He alone must be the source of glory. We let God's light shine in our lives when we let the light of His revelation in the Scriptures reflect off our lives (2 Corinthians 3:18) through the indwelling Holy Spirit. When people see God's word transforming our lives, that substantiates God's word to them through our testimony.