Okay, so imagine you are in a class with 10 other kids and your teacher wants to know what is the middle number when she arranges all your heights from shortest to tallest. Let's say your height is 4 feet, your friend's is 3 feet, and some others have different heights. So, when we write down everyone's height one by one, and put them in order, the middle number is the one that has an equal amount of people above and below it. Now, this middle number is the median number.
Similarly, a median mechanism is a way to find the most appropriate price or value for something when there are many different options. For example, let's imagine a situation where a company is trying to decide the salary for its workers. The median mechanism works by arranging all the salary options from lowest to highest and choosing the middle one as the salary. That way, half of the workers will earn more and half will earn less than the median salary. This is a fair way to decide the salary, and it's called the median mechanism.