This term is used when the result of a certain operation isn't defined. For example, you can't divide one by zero (or any other number by zero), because that would mean that zero times some number equals one; but this is never the case. Or, when calculating with real numbers, you can't take the square root of a negative number, because the square of either a positive or a negative number gives a positive number; no real number, when squared, gives a negative result.
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A term that is undefined mean simply that it is not defined. The prefix un means not, and if you add it to the word defined, ta da, you get undefined.
The mathematical term for "mean" is "mean".The popular, or colloquial term for "mean" is "average".
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A set can be defined or undefined.