As Krazer mentioned, one way of calling it is Animated narrative vignette (ANV).
Another way of calling it is Whiteboard animation.
Whiteboard animation is the process of which an author physically
draws and records an illustrated story using a whiteboard- or
whiteboard like surface- and marker pens. The animations frequently
are aided with narration by script. The authors commonly use stop
motion animation to liven hand drawn illustrations, with YouTube used
as a common platform. It is also used in television and internet
advertisements to communicate to consumer's in a personal way. The
earliest videos made using Whiteboard Animation were published in 2009
on YouTube, used mostly for experimental purposes until developing
into a story telling device, focusing majority on narratives, though
it has many other uses in modern day.
Here's a guideline on how to do a whiteboard animation.