We have investigated the magnetic field dependence of Signal Amplification By Reversible Exchange (SABRE) arising from binding of para-hydrogen (p-H2) and a substrate to a suitable transition metal complex. The magnetic field dependence of the amplification of the (1)H Nuclear Magnetic Resonance (NMR) signals of the released substrates and dihydrogen, and the transient transition metal dihydride species shows characteristic patterns, which is explained using the theory presented here. The generation of SABRE is most efficient at low magnetic fields due to coherent spin mixing at nuclear spin Level Anti-Crossings (LACs) in the SABRE complexes. We studied two Ir-complexes and have shown that the presence of a (31)P atom in the SABRE complex doubles the number of LACs and, consequently, the number of peaks in the SABRE field dependence. Interestingly, the polarization of SABRE substrates is always accompanied by the para-to-ortho conversion in dihydride species that results in enhancement of the NMR signal of free (H2) and catalyst-bound H2 (Ir-HH). The field dependences of hyperpolarized H2 and Ir-HH by means of SABRE are studied here, for the first time, in detail. The field dependences depend on the chemical shifts and coupling constants of Ir-HH, in which the polarization transfer takes place. A negative coupling constant of -7Hz between the two chemically equivalent but magnetically inequivalent hydride nuclei is determined, which indicates that Ir-HH is a dihydride with an HH distance larger than 2Å. Finally, the field dependence of SABRE at high fields as found earlier has been investigated and attributed to polarization transfer to the substrate by cross-relaxation. The present study provides further evidence for the key role of LACs in the formation of SABRE-derived polarization. Understanding the spin dynamics behind the SABRE method opens the way to optimizing its performance and overcoming the main limitation of NMR, its notoriously low sensitivity.