In the same way, let your light shine before others, that they may see your good deeds and glorify your Father in heaven.
Darkness does not have to do anything to achieve it's purpose. It's nature is dark, void of any desire to accomplish or allow light in it's realm to be successful. The Lord desires us to be like Light - associated with Him, therefore working for Him or displaying the "fruits" of our association with Him.
To start off Matthew 5:16, Matthew says, "In the same way..". He is referring back to what he was just speaking about - analogies of us being a light. Matthew 5:14-15 states - You are the light of the world. A town built 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.
Notice that people back then, just like people today, built towns on hills. Why would you do that? Attention. And where there is attention there is the great possibility of investigation. Where there is investigation there is the increased possibility of a town to do business. The town is not hidden sitting on a hill.
Also notice that back then, just like today, when you enter a house the amount of light decreases. Back in the time of Jesus they had oil lamps. Entering a darkened room with a lit oil lamp, Jesus says - Neither do people light a lamp and put it under a bowl. The lamp was lit for a purpose - not to be extinguished, but to supply it's light for the room. In fact, the lamp was placed on a stand in the center of the house/room where it gives light to everyone in the house. So, the benefit was to everybody.
Now we have our main verse - In the same way, let your light shine before others, that they may see your good deeds and glorify your Father in heaven. Wherever God has placed you (work, home, travels, etc), because of your association with God through Christ Jesus - allow your light, which equates to What Would Jesus Do (good deeds) to shine. Why? that they may see your good deeds and glorify your Father in heaven. In addition, allow your light to have the opportunity to shine as brightly and publicly as it would for a city on a hill, as you would shine your light brightly for your family in your home.
Compliments and well-managed pats-on-the-back are one thing, but to hear someone say, "I thank God for you Brother/Sister__________." Or "Thank The Lord for the talent He has blessed you with." - - - - should be even better to hear. As the great Provider, God has provided The Association (Jesus), The Lamp (Us, our bodies) and The Light (good deeds by His strength) - We Just Have To Shine!