Hi there,
For the most part, insulin can be thought of as an anabolic hormone. It encourages the storage of fatty acids and amino acids as triglycerides and proteins respectively. This makes sense because it is predominantly released in the fed state, when metabolic resources are high. This also means that blood sugar levels are high. So insulin wants to lower the glucose level in the blood. It does so by breaking down glucose to produce energy (glycolysis) as well as storing excess as glycogen (glycogenesis). Some cells (eg. RBCs, and to an extent the brain cells) rely on glucose for fuel, so despite having high levels of fats and proteins in a post-prandial/fed state, our body still undergoes glycolysis to fuel these cells. Therefore, it is only the excess that is not needed for fuel, that is stored as glycogen.
Hope this helps!