Energy required to break the "delocalised electron cloud" of benzene
Let's sum it up :)


When cyclohexene is hydrogenated, $\mathrm{-120\, kJ\cdot mol^{-1}}$ is released.
When 1,3-cyclohexadiene is hydrogenated, $\mathrm{-232\, kJ\cdot mol^{-1}}$ is released. That's pretty close to 240, so it looks that the energies for the hydrogenation of the double bonds sum up. So far, we're cool.


Based on Kekule's model of alternating single and double bonds in benzene, we would now assume that the energy for hydrogenation is $\mathrm{ 3 \times -120 = -360 \, kJ\cdot mol^{-1}}$. 

But as your textbook says it's only $\mathrm{-208\, kJ\cdot mol^{-1}}$. 

We must conclude that Kekule was almost right, but the bonding situation in bezene is special. The energy of the molecule is much lower than that of a hypothetical cyclohexatriene. And when it's lower in energy, less is released upon hydrogenation. The difference of $\mathrm{152\, kJ\cdot mol^{-1}}$ is attributed to resonance stabilization.

Edit 1 If that's still a bit unclear with the signs of the energies, we can do some reverse experiments in mind.

Let's take cyclohexane and rip adjacent hydrogen atoms off to generate unsaturated molecules.


We need $\mathrm{120\, kJ\cdot mol^{-1}}$ to make cyclohexane.
We need $\mathrm{232\, kJ\cdot mol^{-1}}$ to make 1,3-cyclohexadiene.
If benzene would be cyclohexatriene, we would need $\mathrm{360 \, kJ\cdot mol^{-1}}$.


But we need less energy to make benzene, because it is more stable than a hypothetical cyclohexatriene. Actually, it is even more stable than 1,3-cyclohexadiene!

Edit 2


  Benzene's actual structure is stable by 152 KJ w.r.t. Kekule's structure. That 152KJ is used for breaking down the delocalised electron cloud of benzene.


Guess what? The teacher is just repeating with other words what we have already worked on our own.

Imagine that you want to convert benzene to the hypothetical Kekule structure.

It's a process that would "consume" energy, $\mathrm{152\, kJ\cdot mol^{-1}}$ to be precise. 

Why is that? It's because benzene has the delocalized $\pi$-system that aromatic molecules use to have. If you want to overcome that and push the stable molecule uphill and turn in into the less stable (= not having the delocalisation) cyclohexatriene, you have to do some work.