What do people mean when they say “shell company”?

u register a company under your name but never open for business at all. No store, no website, nothing, just a name in the registry.

A shell company is a company formed that is not active, and the main purpose is for it to work around laws. While not all of them are illegal, many of them are. In this case, I'm guessing it is illegal because it's sole purpose is to reroute funds in a way that allows the doctors to evade tax.

I'm not entirely sure of how it is being done though!