The “Use AndroidX artefacts” checkbox has appeared in the new project creation window. After reading about this on the Internet, I generally did not understand what AndroidX is. Explain in an accessible language, please. And do I need to include it in new projects?

Answer 1, authority 100%

AndroidX is a new lib with a new namespace to replace the support library API.

android.support 28.0.0 will be the last one. Everything above will be available only through androidx. Therefore, I would advise you to immediately transfer new projects or do on androidX, but the fact that at least allocate time for production and test.

There are good articles on this, how large projects have migrated and finished with their scripts.