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$A$ is a specific event, specified beforehand.

Let's have an example.  Let a random experiment be rolling a six-sided die and looking at what face lands up.  The sample space is $S=\\{1,2,3,4,5,6\\}$.

What is event $A$?  Let's specify it before the experiment is done.  Let $A$ be the event that an even number lands up, that is, $A=\\{2,4,6\\}$.

Say the experiment is done and the outcome is $2$.  Did $A$ occur?  Since $2\in A$, the answer is yes.

Say the experiment is done again and there was an outcome $s$, but we don't know what it was.  Can we say $s\in A$?  No.  Can we say $s\not\in A$?  No.  But we can say that something happened, that is, $s\in S$.