Unknown mean and known variance? Care to explain a little bit?

Hi,
I've been using statistical methods for a while, but the problem is
some of the usual practices common in many textbooks and courses
sometimes get stuck in my head.
There are a lot of statistical tools that can give you critical
information about your data, and when you take statistics as a tool,
usually people are not really bothered if you really know what the
tool is doing for you or not. (well, most of them)
I'd really appreciate your help about a well known scenario: you can
find it in any statistics book, there is a population with an unknown
mean, and a known variance. I'd love to hear a real life example for
this, and an explanation. We have a population, and we do not know the
mean, but the variance is about average deviation from the mean is it
not? How do we know the spread of a population without knowing the
point it is spread around?
Maybe I'm a little bit confused, but I'd really like to get a little
help

All the best
Seref
.

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