How does f(n) < cg(n) specify time?
How does f(n) &lt; cg(n) specify time?

It doesn't. Bachmann-Landau notation is simply a handy way to compare the growth-rate of functions. It doesn't say anything about what those functions mean, and we can be pretty sure that Bachmann wasn't thinking about computers when he came up with it in 1894.
What meaning you assign to those functions is up to you. For example, when analyzing comparison-based sorting algorithms, we typically take $n$ to be the number of elements in the collection and $f(n)$ to be the number of comparisons, or the number of swaps, or the number of comparisons and swaps.
Note also that all of this is always relative to a machine model or a cost model.
As a very simple example, if I were to ask you what is the algorithmic worst-case step complexity for copying a list, you would say $O(n)$. But actually, the correct answer would be &quot;I can't tell you that because you haven't specified the machine model&quot;. Because, for example, in a Turing machine, copying a list is $O(n^2)$, because for each element being copied, the head of the TM has to drive further and further and further to reach the end of the list to write the next element.