What is a correlated subquery?

SELECT * FROM employees e1 WHERE salary > (SELECT AVG(salary) FROM employees e2 WHERE e2.dept_id = e1.dept_id);

How does this correlate?

SELECT * FROM departments d WHERE EXISTS (SELECT 1 FROM employees e WHERE e.dept_id = d.id);

What does this find?

SELECT * FROM products p1 WHERE price > (SELECT AVG(price) FROM products p2 WHERE p2.category = p1.category);

What does this query do?

How does performance of correlated subqueries compare?