Did you have a teacher that sparked epiphanies?

I will answer assuming that "presented material in a way that led to an epiphany" doesn't necessarily mean that the content was presented in a clear way that immediately clicked, but rather in a way that made me think and engage with the content deeply, eventually leading to an Eureka moment. And I'll do this because the only epiphanies I remember came from teachers who presented the concept in such an abstract or weirdly specific way, that the concept wasn't quite clear, until it suddenly was, several many classes later.

One of such examples is a Pre-Calculus teacher that I had. He would focus almost entirely on the physical interpretation of each concept (Physics was his main class). He naturally presented the derivative as a "rate of change" ("rate of change" of position equals speed, "rate of change" of speed equals acceleration, etc). However, once he went over the "mathematical" definition (with very little focus on it) I suddenly realized that the derivative was the slope of a straight line drawn between two points of the function, shortening that interval until it becomes the slope of a line tangent to the curve at that point. The idea of a "slope with just one point" was pure magic. This revelation also made me appreciate Limits a lot more (because up to that point  "Limits" looked like a pointless concept). In this case it was thanks to Limits that you could take a concept that traditionally requires two points to a scenario where you only need one, by virtue of making the distance between them (tend to) zero.

Another example of an epiphany was a class we had on Automata Theory. The teacher would teach the subject using extremely abstract examples (alphabets consisting of shapes, or colors, or just boolean values, and states that were Greek letters or more symbols). It wasn't until almost the end of the semester that I realized that if the symbols were tokens and the states were functions, I could make a language interpreter, or a compiler, or a calculator, or any sort of parser. Furthermore; replacing the symbols for observations or inputs, and the states for actions I could create a simple state-machine-based AI for robots, for example. I think it was a homework assignment involving parsing binary strings that made me realize this. Whatever the case, the vast array of applications that suddenly popped up in my head absolutely blew my mind.

It doesn't necessarily have to be a teacher. I just recently discovered that LTspice has the same effect...

Yes - his name was Mr Woolard, he taught maths and rugby football while I was in the sixth form studying 'A' levels. Up until then I'd been pretty dumb at maths. With his teaching lots of things suddenly clicked, such as quadratic equations and those three equations that bring speed, acceleration, and distance together. He introduced us to logarithms, sines, cosines, etc., and we were given slim volumes of log tables.

Then the school set up a special offer for students enabling them to buy Thorntons slide rules at bargain prices. What a revelation that was! I still have mine, in it's black plastic case, and it still works. A wonderful machine that needs no batteries. And the knowledge I gained from it came in very useful when I bought a Sinclair Scientific calculator, with it's Reverse Polish notation. Sadly that no longer works even though I tried it with new batteries. The constants are still readable, I coated them with a thin layer of Conformal Coating well before they wore off on other Scientifics.

My first 'company calculator' had lots of sliders on the front and a large cranking handle on one side. I was able to do quite complicated calculations on it. But it was a shared device, used by the whole department. And then another special offer, this time from a company called Texas. I've still got one and it still works 60 years later. Thank you Mr Woolard, you guided me into a great life. I don't know what powers it but it has never needed new batteries.

Ah yes the little book of log tables - to be carried everywhere. You could always tell who the engineers were because we carried slide rules.

One surprisingly useful concept that clicked after just being mentioned in an off-hand way was dimensional analysis, where one could solve problems or at least do a sanity check on answers just by figuring out if the units of the result were correct.

The one that comes to mind was at the Army's Prime Power course when we did operations - running generators in parallel (many years ago).  I think her first name was Pam.  I can't remember her last name right now, but she was one of maybe two ladies in that career field.  Anyway, paralleling to the infinite grid (utility) is crazy simple.  Paralleling to another generator that may not be of similar size... much less so.  What you do to one impacts the other.  Sitting around the breakroom table, she explained the cause and effect in "simple terms" that turned the light bulb on for many of us.  Operating became much easier after her explanation. 

After having high school physics, 3 or 4 semesters of college physics, during an engineering statics & dynamics class, a prof looking at us one day and said " didnt anyone ever mention that another name for moment of force is torque ? "  The entire classroom lit up. Now it all made sense.   

Remember when calculators (and slide rules for that matter) came with cases with belt loops?