COSY (Correlated Spectroscopy) was one of the first multidimensional experiments.  Cross peaks in COSY are between protons that are coupled. COSY tells you "what proton is coupled to what proton." Protons that are two, three, or sometimes four bonds apart may show cross peaks. The magnitude of the couplings affects the peak intensity. For small couplings, such as four-bond couplings, or three-bond couplings where the dihedral angle is near 90 degrees, the peak intensity will be low. The peaks along the diagonal are the projection of the one dimensional spectrum. The cross peaks are symmetrical about the diagonal.
Below is a 500 MHz spectrum of sucrose in D2O. Some cross peaks between protons that are separated by 3 bonds are emphasized. For example, the red cross peak labled 1 links proton 1 and proton 2.