'Doodle' is the general term, 'zentangle' is the name of a company all about zen doodling. If you google each term you'll find tons of examples online.
What is it exactly? It's methodical doodling.
Whatever the name, it's easy to learn and it's relaxing. You don't even have to plan ahead; you can just be in the moment and follow the steps, so your final design is a surprise!