There are many references to it in public discussions, but trying to learn about it from Wikipedia is like reading in a new foreign language.
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It’s a deliberately minimal theoretical computer, which is used to reduce the complexities of any computer down to a very simple model that you can mathematically analyse.
Doing so allowed people, including Turing, to formulate mathematical answers about what a computer can or cannot be used to compute. The simplicity of the “machine”, which is just a theoretical model, not an actual machine, meant that you could actually prove some theories about it. Because the machine is also “mathematically equivalent” to every old or modern computer too (and that was quite easy to prove itself) it lets you expand those same theories to “real” computers of all kinds (we believe even quantum computers follow the same kind of rules).
It’s like boiling down a solar system to a few balls spinning around and then using that model to make predictions, assumptions and insights about how our solar system works, but in a mathematically-rigorous way.
Specifically, Turing machines can tell you what is “computable” and what is not, and there are literally some things that we then thought of that are not “computable” at all.
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