A simple way to detect motion (naively intended as pixel intensity variation) is by using background subtraction.
Check this OpenCV tutorial. Note that one of the main assumptions here is that the scene background remains 'static'. So every time an object comes or moves in the scene, you can detect it, and for example, track it using a centroid given by the average of the pixels mask.
See Motion Detection: Part 3 - Background Subtraction for a concrete example.

If you want to consider just a part of the image, do as suggested in the other answers.