Additive manufacturing, including laser powder bed fusion, offers possibilities for the production of materials with properties comparable to conventional technologies. The main aim of this paper is to describe the specific microstructure of 316L stainless steel prepared using additive manufacturing. The as-built state and the material after heat treatment (solution annealing at 1050 °C and 60 min soaking time, followed by artificial aging at 700 °C and 3000 min soaking time) were analyzed. A static tensile test at ambient temperature, 77 K, and 8 K was performed to evaluate the mechanical properties. The characteristics of the specific microstructure were examined using optical microscopy, scanning electron microscopy, and transmission electron microscopy. The stainless steel 316L prepared using laser powder bed fusion consisted of a hierarchical austenitic microstructure, with a grain size of 25 µm as-built up to 35 µm after heat treatment. The grains predominantly contained fine 300–700 nm subgrains with a cellular structure. It was concluded that after the selected heat treatment there was a significant reduction in dislocations. An increase in precipitates was observed after heat treatment, from the original amount of approximately 20 nm to 150 nm.