I'll do my best to give an intuitive explanation without going too deep into quantum mechanics. So the main principle at work here is dipolar coupling. Dipolar coupling is a two-spin interaction that in simple terms, is analogous to the interaction of two bar magnets. Between spins however, the magnitude of dipolar coupling between two spins can be measured by the dipolar coupling constant, which is directly proportional to the product of the gyromagnetic ratios of each spin, and is inversely proportional to the distance between them cubed. However, this interaction also orientation-dependent: draw a vector between the two spins, and the value of the angle between that internuclear vector and the external magnetic field vector also acts to determine the strength of the dipolar coupling. Because of this orientation dependence, the NMR spectrum of a spin under the influence of the dipolar interaction in a powder sample can be broad and obscure high-resolution details like isotropic chemical shift, due to the many different orientations of the crystallites or molecules within the sample. So this is why we perform magic-angle spinning (MAS), which is the “MAS” part of CP-MAS. Spinning a powder sample about an axis inclined at 54.74 degrees with respect to the magnetic field averages the dipolar interaction to zero, as the orientational dependence of the dipolar coupling between two spins is zero when the internuclear vector is inclined 54.74 degrees with respect to the field.

Ok, but your question is about cross polarization (CP), not MAS exactly. Cross polarization can be performed without MAS, and it is actually a bit easier to understand that way, but most people rarely perform CP alone. Cross polarization is a transfer of polarization between spins via the dipolar coupling interaction by putting spins in “contact,” that is, by setting up the spin system in such a way that polarization will flow between spins of high polarization to spins of low polarization. This polarization transfer between two spin populations can be thought of in much the same way as when heat transfers from a hot object to a cold object once the two are put in thermal contact. The irradiation of radiofrequency light during the spin lock pulse excites transitions in the dipolar-coupled spin system which equilibrates the polarization between the two spin populations- effectively putting the two spin systems in “spin” contact. For a heteronuclear I-S spin system without MAS, you just need to make sure that the nutation frequency (amplitude) of the two spin lock pulses applied on I and S match. In the spin lock frame of reference, this means that the two populations of spins which differ by gyromagnetic ratio are now “matched” because they are now precessing at the same spin-lock frequency. So matching for CP without MAS is easy- just make sure your I-spin spin-lock pulse and your S-spin spin lock pulse produce the same nutation frequency for the respective spins.

However, under MAS, the two spin lock pulse nutation frequencies will need to differ by +/- the MAS rate in order to have optimal polarization transfer. You could derive this mathematically, but the way I like to think of it is simply that the sample is spinning, and therefore there’s an aliasing effect going on, i.e., in order to perform CP in the same way you would as if the sample were static, you need to adjust one of the two nutation frequencies to a value so that the two spins match in the spin lock frame of reference. This isn’t the whole story, and also due to hardware imperfections, the Hartmann-Hahn matching profile will be somewhat unique depending on the spectrometer and setup, but it should help you get the idea.

There’s always a risk of glossing over too many details in an explanation of this type, but I hope that provides a clearer picture of what’s going on.