What is 不懂 vs 不懂了

If you “never got it,” say 不懂.
If you “once got it but now it’s gone,” say 不懂了.

1. 不懂 (bù dǒng)
A plain statement: “I don’t understand.” No hint of any change.
Ex:
A：这道题怎么做？
B：我不懂，你能再讲一次吗？
2. 不懂了 (bù dǒng le)
The particle 了 marks a change of state: “I used to understand, but now I don’t” or “I’ve lost the thread.”
Ex:
a. 他越讲越快，我原来还能跟上，现在完全不懂了。
b. 小时候觉得这首诗很美，长大后再读却不懂了。

The thing about end sentence 了 is that it expresses currently relevant state, that is, something that is in some way relevant to the ongoing situation or conversation. So while it can express change or new emergent state (I no longer understand), it could also indicate that this statement is somehow relevant to the thing we're discussing right now. It is completely non-mandatory but Chinese use it very often.

了at the end could mean many things: these things you said I do understand, but this last one 不懂了; or, some you you say this guy understands what you are saying to him, others say he doesn't; in the end the truth is that he does NOT understand (不懂了) - the 了 here is pretty much an emphasis that this is indeed the true, relevant state of things, and it adds a bit of an emotional connotation to the statement.

So the thing is that you can pretty much always or at least in many, many cases say stuff without the 了 at the end. The thing is that, it gets used A LOT by native speakers and it adds some subtext to the main message.