The van der Waals material CrSBr stands out as a promising two-dimensional magnet. Especially, its high magnetic ordering temperature and versatile magneto-transport properties make CrSBr an important candidate for new devices in the emergent field of two-dimensional magnetic materials. To date, the magnetic and structural properties of CrSBr have not been fully elucidated. Here, we report on the detailed temperature-dependent magnetic and structural properties of this material, by comprehensively combining neutron scattering, muon spin relaxation spectroscopy, synchrotron X-ray diffraction, and magnetization measurements. We evidence that this material undergoes a transition to an A-type antiferromagnetic state below $T_{\rm N} \approx$ 140 K, with a pronounced two-dimensional character as deduced from the determined critical exponent of $\beta \approx $ 0.18. In our analysis of the field-induced metamagnetic transition, we find that the ferromagnetic correlations within the monolayers persist clearly above the N\'eel temperature in this material. Furthermore, we unravel the low-temperature (i.e. $T < T_{\rm N}$) magnetic hidden order within the long-range magnetically ordered state. We find that it is associated to a slowing down of the magnetic fluctuations, accompanied by a continuous reorientation of the internal magnetic field. These take place upon cooling below $T_s$ $\approx$ 100 K, until a spin freezing process occurs at $T$* $\approx$ 40 K. We argue this complex dynamic behavior to reflect a magnetic crossover driven by the in-plane uniaxial anisotropy, which is ultimately caused by the mixed-anion character of the material. Our findings indicate that the magnetic and structural properties of CrSBr widen its potential application as a component for spin-based electronic devices.