In a TV Show I am watching (Doctor Who) there is moment where a character says
There's such a thing as** too keen.
I am wondering what does the "There's such a thing as too [adjective]" mean?
Backing up a bit: "there's such a thing as X" means that X exists. "There's no such thing as X" means that X does not exist.
There's such a thing as a zebra, but there is no such thing as a unicorn.
As for "such a thing as too...", it's a way of saying that too much of a good thing is a bad thing. For example, on my fifth birthday I learned that there was such a thing as too much ice cream. Unfortunately, so did the living room carpet. :)
Now, have a look at these:
There's no such thing as too quiet.
There's such a thing as too quiet.
Both of these sentences have the implied assertion that quiet is desirable. However, the first sentence is saying that absolute silence is the speaker's ideal, and the second is saying that while a certain level of quiet is desirable, too much quiet isn't.
There's such a thing as too X, is a rhetorical device - a figure of speech - that highlights something that someone is doing by pretending they've never heard of X. Generally, it's a normally positive adjective, turned negative by having too much of it.
If you were riding a bicycle in heavy traffic without a helmet, I might say "there's such a thing as too brave"
If you were eating too much food, I might say "there's such a thing as too full"
If you were on fire, I might say "there's such a thing as too warm"
In each of these cases, the emphasis (and pitch movement) is on too, signalling that this is the news - you can have too much of a good thing.
The adjective in "there's such a thing as too [adjective]" is something which is usually regarded as a positive. The expression "there's such a thing as too [positive attribute]" expresses the contention that the positive attribute becomes a negative one when had in excess, or as the English idiom has it, "too much of a good thing". (Compare with the contrary stock phrase, "There's no such thing as being too thin or too rich.")
In the circumstances in which the expression is used "out of the blue", that is, without preamble or obvious context, it comes with the added connotation, "You seem to be behaving as if you thought it was good thing that you are so very [positive attribute], but I think you're becoming insufferable in how [positive attribute] you are."