Strictly speaking, $O(f(n))$ is a *set* of functions. So the value of $O(f(n))$ is simply *the set of all functions that grow asymptotically not faster than $f(n)$*. The notation $T(n) = O(f(n))$ is just a simplified way to write that $T(n) \in O(f(n))$. 

Note that this also clarifies some issues of the $O$ notation as it is normally used. 
For example, $n^2 \in O(n^3)$ but $n^3 \notin O(n^2)$. So you can write $O(n^2) = O(n^3)$, but you cannot write $O(n^3) = O(n^2)$, even though one normally expects $=$ to represent an equivalence relation (in particular, symmetric).