What is Two-dimensional spectrum, cross peak, diagonal peak?

A two-dimensional spectrum is recorded by repeating a pulse sequence with an incremented delay $t_1$ before the acquisition time $t_2$; a double Fourier transform gives a map of intensity against two frequencies. A cross peak at $(\delta_1, \delta_2)$ shows that the nuclei at $\delta_1$ and $\delta_2$ are connected (by a coupling or by proximity); a diagonal peak at $(\delta, \delta)$ belongs to a single nucleus.