"As I understand it"?
Hmmm. I never see functions as explainable individually. I know that typically, Te is described as an action-oriented, "get things done", plan everything and for every contingency "personification of systems, organisation and characterisation" type of function, but that seems more like an external descriptor of the function rather than the experience of it.
I do make lists. I am organised. I do have flowcharts, mind-maps, concept maps, schematics, calendars and like making plans and detailed schedules. But I would say that these are more tools to facilitate what I want to get done because I am usually juggling lots of stuff and it's impossible to keep track of all the details associated with disparate aspects of my life. I don't organise for the sake of organising, or systematise for the sake of it unless it's one of the things that I'm obsessive-compulsive about. It's just the quickest way to get things done, track progress and reduce anxiety (not sure how much my OCD factors in here).
Usually, I have a detailed plan based on everything that I imagine could possibly happen, and if things start to go wrong or the plan isn't working, I go back to the underlying assumptions when I formulated the plan and use that to adjust plans slightly. Usually, like moving the top of a pendulum, when I change the way I see the situation, everything that comes after (or the movement of the pendulum base) is immediately self-evident. The plans aren't really fixed, even though people who look at the schematics I draw or lists that I make often assume that they are.
People earlier in the thread spoke of Te as the driver to "get things done" or the actionable function. I see Te more as a means of externalising what is internal. With Ni as my dominant, it's not possible to verbalise the way that I turn a situation over in my head and the various perspectives and possibilities I simultaneously evaluate, integrate and discount. Often, when thinking about things, my concepts are in a very visual form, like turning a 3D figure around in my head while running if/then/else probabilities, and evaluating the probabilistically likely final outcome, almost as if running a monte carlo simulation. The only way to communicate what goes on inside is to categorise it, define things and weigh them externally.. which takes time, effort and energy.
Sometimes, when I try to classify and problem-solve using standard definitions and linear logic, I get stuck in a loop. It often requires actively disengaging logic and doing something completely different before my subconscious kicks in and I get the answer when I'm half-asleep or running or too tired to think. Then the answer illuminates the initial missed assumption and it's all too easy to explain how to get there.
In the opposite direction (how Te affects my dominant function) I think it's also important to note that the categorisation slant of Te also colours the information that Ni takes in and builds relationships between. Some people mentioned seeing objects in terms of their potential and not what they were made to do - that comes from the categorisation process, I think, and counter-intuitively helps with creativity and being flexible. If you need to get 2L of fluid from A to B and you only have a groundsheet, you won't be trapped if you see it as "I need something waterproof" as opposed to being limited by the idea of a hollow round cylindrical object like a bucket. That has often helped me to visualise and build systems to solve a specific problem where there weren't any solutions before.