How long is a piece of string is a phrase used to avoid estimating the size, length or duration of something. Instead, it embodies the sense of indeterminate quantity.
For example,
Q: "How much time will it take to fix?"
A: "I don't know how long is a piece of string?"
It is used in the context of an unanswerable question because though a particular piece of string can be measured, just knowing that it is a piece of string tells you nothing (or almost nothing) about its length.
The quantitative answer is not readily known, and there is an implicate understanding that the answer will be difficult to find given the information available. So, if someone were to ask you, "how long is a piece of string?" the only honest answer is that you do not know. It's a different question from "how long is this piece of string?"
I prefer to answer this question more literally by saying, "a piece of string is twice as long as half its length".
