I have been reading this tutorial on time complexity, and I am a bit puzzled on its explanation of big $ O$ notation. It writes:

$ O(g(n)) = $ { $ f(n)$ : there exist positive constants $ c$ and $ n_0$ such that $ 0 \leq f(n) \leq c*g(n)$ for all $ n > n_0$ .

The way I understand it, $ c*g(n)$ denotes $ c$ multiplied by $ g(n)$ . If this is the case, then how does the above expression specify time, and not just that $ c*g(n)$ is greater than $ f(n)$ ? Or am I incorrect, and this is some notation I don’t understand? My understanding of time complexity is very rudimentary, so forgive me if this is just a stupid mistake on my part.