What an asshole way of explaining it. For practical purposes (don't @ me if this is technically wrong, I don't give a shit) it's a description of how the cost of an algorithm grows with the size of the input. For example if the cost doubles every time the input increments then it's O(n^2). If the cost increases in step with the input size then it's O(n). Simples.
In computer science f(x) is often some complexity function, like number of some specific operations when running an algorithm to completion.