The term modern physics refers to the post-Newtonian conception of physics. Put simply, modern physics deals with the underlying structure of the smallest particles in nature ("quantum" mechanics), as well as a rigorous understanding of the fundamental interaction of particles, understood as forces. Small velocities and large distances is usually the realm of classical physics. Modern physics often involves extreme conditions; quantum effects usually involve distances comparable to atoms (roughly 10 m), while relativistic effects usually involve velocities comparable to the speed of light (roughly 10 m/s).
The term "modern physics" implies that classical descriptions of phenomena are lacking, and that an accurate, "modern", description of reality requires theories to incorporate elements of quantum mechanics or Einsteinian relativity, or both. In general, the term is used to refer to any branch of physics either developed in the early 20th century and onwards, or branches greatly influenced by early 20th century physics.