Some physical processes, especially quantum processes such as nuclear reactions, are inherently probabilistic, and can only be described statistically.
Many large classical systems (e.g. a volume of gas) have so many variables, or degrees of freedom (positions and velocities of every molecule), that an exact treatment is completely intractable, and in any case, not really useful. A statistical approach works very well, since the number of degrees of freedom is extremely large.
Statistical mechanics can be used to model both these types of systems.