After Effects - Simple Lighting Effects
This is a simple animated lens flare. The specific lens flare they use is likely from a package of lens flares you pay for (a plugin) made by Andrew Kramer over at videocopilot, specifically: https://www.videocopilot.net/products/opticalflares/  

To create custom light flares without the need to pay for them, I'd recommend watching this video: 
                
            

You simply create the object, the flare in this case, and animate its' position. Do you know how to do that?