I came across this sentence:
"The biggest risk you will ever take is not taking one at all."
I am unable to understand what does one at all mean in the statement context.
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The words "at all" could be removed from the sentence without any real change in meaning:
The biggest risk you will ever take is not taking one.
which would mean the same thing as:
The biggest risk you will ever take is not taking any risk.
In other words, if you are too cautious all the time, that becomes a risk in and of itself.
The line you ask about reminds me of another similar quote:
The only thing we have to fear is fear itself. (Franklin D. Roosevelt)
As Janus said in a comment, the meaning of at all is idiomatic, but you need to know to look for the phrase as a whole.
• (used with a negative or in a question) in any way whatsoever or to any extent or degree ⇒ "I didn't know that at all"
• even so; anyway ⇒ "I'm surprised you came at all"
The phrase at all usually emphasizes the text that precedes it.