When a doctor says that something is a "routine procedure", it means that he or she often does it, and it's nothing new or scary.

The word "routine" means "usual". You might know that "routine" can be used as a noun:

So, have you settled back into the routine?

But it can also be an adjective like in the example at top.

When you're talking to a doctor, a "procedure" usually means a surgical procedure. Or, in other words, some kind of surgery. In general, a "procedure" is a set of actions that follow specific steps. Here are some other common types of procedures:

a legal procedure

a testing procedure

a company's standard operating procedure