How to create this effect?
It looks like the contents of the bubble is a zoomed in view of a video clip or a series of still frames. 

The animation uses manually set keyframes to alter the position of the clip to create a pan effect. The cursor is also animated using manual keyframes. The acceleration of the pan is smoothed, probably with 'Easy Ease' transitions.

The video is then masked using an ellipse graphic with a shadow included, which can be easily be created in Illustrator.



It is possible to replicate the effect by taking a clip of a screen recording and tracking the motion of the mouse cursor to directly follow the action. This would be a lot easier to do (provided the cursor does not change and is always visible) but the results would be very rough.

The best way to replicate this effect would be to add manual keyframes as shown in the example video.