For simplicity, imagine that a strategy is just to pick up a number. Now think about the value of increasing the strategy of player 1 assuming player 2 strategy is being held constant. If the value of increasing the strategy is higher the higher is the strategy of player 2, we say the payoff of player 1 is super-modular in the strategies. If this happens for both players, their strategies are said to be complementary. If payoffs are differentiable this is the same as the cross-partial derivatives of payoffs being positive: $\frac{\partial u_i}{\partial s_1 s_2}(s_1,s_2)\ge 0$ for $i=1,2$.
In the case of ta finite game like the Prisoners Dilemma, we must somehow order the strategies. Let's say that cooperation is low strategy and defect is the high strategy, $CD$) then you still have the same inequality as before. Not all Prisoners Dilemma games are super-modular.
$$D>C,\;\text{super-modular}\Longrightarrow \begin{matrix}
& D & C \\
D & 0,0 & 3,-7 \\
C & -7,3 & 2,2
\end{matrix}
$$
$$D>C,\;\text{not super-modular}\Longrightarrow \begin{matrix}
& D & C \\
D & 0,0 & 7,-1 \\
C & -1,7 & 2,2
\end{matrix}
$$
Super-modularity is more interesting/useful in the context of coordination or matching games than in the prisoners dilemma because it implies the set of Nash equilibrium is a lattice (nice math object). In the case of the prisoner dilemma, there is only one Nash equilibrium so we are not interesting in talking about the set of equilibria...