I mean, my interpretation is that the question Turing tried to answer is equivalent to "How can we determine whether machines understand humans/human thought?"
This only works when both systems can talk about pretty much arbitrary things, but if you want a more general method for less complex systems, perhaps having one system simulate another system is sufficient. (Which is also another Turing invention)
At this point, I am unaware of a better definition. I know the Chinese Room argument (and I disagree with it), but I'm not aware whether the proponents of that argument have a better definition of understanding other than "well, the Turing Test isn't enough"...
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PS: Interestingly the issue of compression is highly relevant regarding the Chinese Room argument -- the essential element in the Chinese Room argument is that the information is not compressed...