Definition: A thinking tester is a tester whose main value comes from thinking, questioning and investigating, rather than following scripts. The term is used to contrast skilled testing with the idea that testing is low-skilled, repeatable work that automation could simply replace.
So what? How testers are seen affects how they're paid, hired and promoted. Showing that testing depends on thinking helps change the perception of testing as low-skilled work.
Examples: A tester questioning a requirement and finding a risk no scripted test would have covered. A team valuing exploratory testing sessions alongside automated checks because they find different kinds of problems.