Professor Jackie Andrade at the University of Plymouth tested out the theory that doodling could improve attention and memory (by 30%) in certain circumstances (like listening to a long boring meeting).
She speculated that our minds wander when we are bored or doing simple tasks, and this interferes with our ability to listen and pay attention.
Doodling might keep our attention focused on the task at hand (listening) rather than going totally off track.
Certainly, this is what I found when listening to some speakers.
You can read about the results here: