Author's note: I myself am an INTJ, therefore Ti is not in my main function stack. I have compiled the best information I can from what I found from Career Planner, The Career Project, Personality Junkie and Quora answers, however, I cannot provide any personal anectodes.
Introverted thinking is an introverted and judging function. It is focused on impersonal analysis, categorisation, and evaluation based on a set of logical, subjective principles. Ti users generally consider many different solutions before choosing the best one, whereas extraverted thinking (Te) users tend to find it more important to be done than to find the best solution.
I found this here: "I need to understand a rule or 'fact' in my own way. I have to research and experiment and decide whether this truth really lines up with logic and my principles. Sometimes this irritates people because they want me to take certain rules and 'empirical evidence' at face value."
Ti users develop complex systems in their heads, which explain how things work. For people with Ti as their dominant function (INTPs/ISTPs), when they come across a new piece of information, they will test it against their internal models to see if it fits. If it fits, they will store the information in the correct category. If it does not fit, but they still think that the information is correct, they might completely reevaluate their mental model to understand why it does not accommondate the new information.