Y is the measurable outcome ("has/has not ADHD", household income, whatever), right?

What's confusing GP and me, I think, is what is X here and what does having more or less of it mean?

Both x and y have to be measurable. Here, x could be score on IQ test. Since score on IQ tests are somewhat well correlated with academic achievement, then more x (higher IQ score) means more likely y (higher academic achievement). It’s important to note that it’s only more likely. Correlation is a predicter of a relationship given a population, not a dictator of outcomes for individuals.

Yeah exactly

What is Y in this graph please? Possibility to have correlation?

X is one variable and y is another. The correlation is, given x, how likely can we predict y.

So if x is IQ score, and y is income, and if there is a strong positive correlation, then given high IQ (x) we can confidently predict high income (y).

If there is no correlation between x and y, then given x, we cannot predict y.