In the Free Variable article on Wikipedia, it lists these:
as variable-binding operators. I have seen all of them during my math studies, except for the psi operator. What does $\psi x$ mean in this context?
I don't know what was intended by $\psi$ here, but some Wikipedia archaeology reveals that it was introduced in this edit, and the same user tried to remove it again one minute later. They made a mess out of the removal, and Michael Hardy undid the mess, leaving in the $\psi x$ with no explanation. None is likely forthcoming, because the user who added the $\psi x$, back in August 2008, has not been back to Wikipedia since.
In short, it is most likely a piece of Wikipedia nonsense. Unless someone posts a definitive answer here, I will shortly remove the $\psi x$ from the Wikipedia article.
As a consolation prize, here are some other variable binding operators you may not be familiar with, which are not in the Wikipedia article:
Commonly-used quantifiers that do not seem to have any standard compact notation include "almost everywhere" and "all but finitely many".
My first impulse in seeing ‘$\varphi x$’ is to read it as a variation on the logical schema (‘$\varphi(x)$’, ‘$F x$’, etc.), which, if that was the intented meaning, should, I believe, preclude it from a list of variable-binding operators. I would vote up for removal from the article if I could.