There's more than one type of 2D NMR spectroscopy. The most common are the COSY (homonuclear, 1H vs 1H) and the HETCOR (heteronuclear, 1H vs 13C).
Since a COSY has the same spectrum on the X- and Y-axes, there is a diagonal where each signal lines up with itself (if that makes sense). Those aren't very interesting, but the off-diagonal signals are useful. These tell you which hydrogens are splitting each other. For simple structures, you can often deduce this information from a 1D experiment, but for more complicated structures, a COSY can be very helpful.
The HETCOR plots a 1H vs a 13C spectrum. Since the two spectra are different, there is no diagonal. Each signal in the box tells you which carbon each hydrogen is attached to and vice versa.