what exactly does the VAR function do?

It declares a variable or array. It's necessary to declare variables only when using OPTION STRICT, although always declaring variables is a good programming practice.

I'd call that the VAR command instead of the VAR function. There is a VAR() form but it does something entirely different.

VAR can be used the same way as DIM (though some people tend to use DIM for arrays and VAR for other variables) VAR() is a function that returns a reference to a variable (not the value) for example, you can do INC VAR("X"), or VAR("X")=100