Analysis and evaluation to form judgement and reasoned conclusions.
A context where I used this skill:
While I do use this tool set all the time, allow me to provide one concrete example. I came into a project that involved a computer-‐‑to-‐‑computer system in which the data was generated by a user in a name-‐‑value pairing that our system would interpret. I came into the project after another tester had developed a web page to send these values in an automated fashion and save those test values to a database. I didn't know much about the project so I started asking questions. I asked how he could detect duplicate test cases were entered. He said that was done manually. I asked how he intended on knowing what was tested. He said he would read the output of the tests. I asked how that would help and he said he could tell from the response what was sent in. I asked what if the test failed. He didn't know what he would do then. I asked what validation was being done. He said that was manually done with no validation. I kept asking questions, and kept finding that the testing did nothing, as there was no way to know what was being tested. Ultimately, we scrapped the entire project as it was not built in a useful manner. I wouldn't have known that the testing wasn't useful until I had asked in depth questions along with follow up questions.
How I'd recommend someone learn this skill:
There are many sub skills within the process of critical thinking. Some involve positive elements such as investigation and some involve negative elements such as finding biases. When looking at a knowledge source, consider what the purpose the author intends. In marketing work, consider how it might affect you emotionally, and why the author would do that. Ask where the data came from and check that data to validate or invalidate the conclusion. Now once you find you can start asking interesting and in depth questions from other sources, ask these same questions about your own work. Why should the developers fix that bug? What is the purpose of this test report? What value do I gain from asking this question of the product owner and is there a more effective way to ask the question? What assumptions are built into my question and are they reasonable? Keep asking questions and when you run out of questions start looking for new questions to ask. Adapt your process and investigate, look for bias and assumptions (including your own). Read David Levy's Tools for Critical Thinking book.
Tools for Critical Thinking: Metathoughts for Psychology by David Levy
Critical Thinking: Basic Questions & Answers by The Foundation for Critical Thinking
Critical Thinking by Wikipedia