There is nothing like having to drag a window to the second screen and then trying to find the play button, volume or full screen button on the remote screen. 

You can embed your videos in a PowerPoint presentations or another "presenter" program but here is a very simple (and free) solution.

Step 1:  download and install VLC. Look on videolan.org

Step 2: download VLP and extract it to a location of your choice, for example in C:\Program Files (x86)\VideoLAN. 

VLP stands for VideoLan Presenter. It looks like this:

The rest is pretty self-explanatory...

You can create a shortcut to VLC on your desktop and drag one or more videos to it and voila!

Have fun, and most of all, peace of mind with a sleek, lightweight and free solution.