This is the new app of Google for the world-cup:
What program is Google using to design these drawings? Or what's the name of that type of design so I can try to learn it?
I'd probably call these type of illustrations 'vector illustrations', because they look like, at least regarding the original source files, they could be scaled up easily. If I were looking for them, to use on for example on a website, I might also search for the term "flat".
You can use different programs to make them, if you are looking for a free solution I strongly recommend Inkscape. If you want a more complete / professional software, then Adobe Illustrator is probably your best option. But you can really create these using any software.
For the most part, what you will be doing is creating points and lines/curves between them. It's best if you organize your drawings in layers, so you can for example start with the backgrounds and then just add shapes on top of them. An easy way to start working with these is, in my opinion, to re-draw some of them so you get used to tracing shapes.