Do I understand the concept of closures?

So, just so I have a clear understanding of what a closure is, I'm going to attempt to explain it

function retirement(retirementAge) {
    var a = ' years left until retirement';
    return function(yearOfBirth) {
        var age = 2018 - yearOfBirth;
        console.log((retirementAge - age) + a);
    }
}

var retirementUS = retirement(66);
retirementUS(1989);

When creating the retirementUS variable, the outer retirement function runs and the parameter (66) is passed. That function is then popped off the execution stack and the inner function is now stored in the retirementUS variable. BUT the variable 'a' is stored in memory - thats why the inner function has access to the variable, even AFTER the outer function has returned. You are then able to pass the yearOfBirth parameter to the retirementUS function. The benefit of this, is that the variables are kept private and can't be changed by other code.

Is this right?