Just like the term
Rubber duck debugging, which is in software engineering, a method of
debugging code. The name is a reference to a story in the book The Pragmatic Programmer in which a programmer would carry around a rubber duck and
debug their code by forcing themselves to explain it, line-by-line, to the duck. Many other terms exist for this technique, often involving different inanimate objects.
The "coffee mug debugging" is the same method of debugging code with which developers force themselves to read and explain their code line-by-line, to the coffee mug. There are developers who calls this planted plot debugging as well. But "coffee mug debugging" seems more convenient at this century since it's easy to find a coffee mug for a developer than a "rubber duck" or "planted plot".