Peaks along the diagonal refers to the diagonal line drawn from the bottom left corner to the top right corner. You always get a diagonal peak for every resonance in the spectrum. There are four resonances in ethyl benzene spectrum (including TMS), and you get four diagonal peaks. Off-diagonal peaks are any peaks that are not along the diagonal. If you look at the spectrum on the link, you see that there is a set of four that form a sort of square near the top-right corner of the plot. Two of these are your on-diagonal peaks for the benzene ethyl group. The other two, off-diagonal, show that the two groups or protons are coupled together, as you'd expect. There is no off-diagonal peak linking the aromatic resonances to those of the aliphatic chain (if there were, you would get two off-diagonal peaks, one in the top left corner of the plot and one the bottom right, which link these two). This makes sense because the aliphatic and aromatic protons are not coupled.
If this isn't making sense, I will try to show it graphically for you.