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The honeycomb lattice Heisenberg model is uncomplicated: only nearest neighbor Heisenberg interactions are considered; there is no frustration, and the ground state at T=0 is the Néel state.  The experimental realization of the honeycomb lattice Heisenberg model discussed here is the rare earth halide YbCl₃.  We present a comprehensive study of the spin excitation spectrum of YbCl₃ using inelastic neutron scattering measurements under applied magnetic fields in tandem with linear and nonlinear spin wave theory calculations. By examining the spin excitation spectrum above the saturation field where the physical behavior is explicitly classical and linear spin-wave theory is essentially exact, we accurately determine the dominant nearest-neighbor Heisenberg interaction. Below the saturation field, we reveal a field-dependent energy renormalization of the entire magnetic spectrum -- the sharp spin-wave modes as well as the multimagnon continuum. This renormalization is a quantum effect that can be accurately captured by the first 1/S correction in nonlinear spin-wave theory. Furthermore, we find that the application of a magnetic field induces a qualitatively new sharp feature inside the multimagnon continuum -- the lower edge of a specific two-magnon component -- which demonstrates that structures within the multimagnon continuum can occur over a wide experimental parameter space and can be used as an additional means of identifying quantum phenomena.