It is best to think of "random" as a technical term in mathematics (from probability theory). We apply that mathematics to real world phenomena where we find that appropriate. We find it natural, in such circumstances, to apply the word "random" to what is modelled.
There is also some colloquial use of the word "random". One common instance of this is in the local port used for a network connection. If you look at the output of "netstat -n" on your computer, you might see something like this:
1.2.3.4:1179 207.36.231.74:80 ESTABLISHED
where the "1.2.3.4" is your local IP address, and "207.36.231.74" happens to be the IP address of evcforum. The "80" is the port you are connecting to. The "1179" is the local port you are using for this connection. The local port is often called a "random port". On a window box, the first connection ever made will use 1024 for a random port, 1025 for the next random port, 1026 for the next, etc. That is, these are usually assigned sequentially. Sequential is pretty neat for something called "random.". The term "random" is used here to mean that there is no significance to the particular choice. It could be anything. It happens to be done sequentially, because thats the easiest thing for software to do.
For the term "random" as used in "random mutation", you should simply take that as saying that there is no rhyme or reason for this particular mutation rather than a different one. Or, at least, there is no known reason or mechanism that preferred this mutation over a different one, and all the evidence suggests that there could not be a mechanism behind the choice.
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