depends on the problem you are investigating. Mathematically, it is to find the minimum value of the function. For certain physical problems, it could imply the lowest energy state or the equilibrium state of the system.
Generally, calculations are done to calculate energies, structures and other parameters. For example, in thermodynamics, if you have an equilibrium between compounds A and B and you want to know the equilibrium constant, calculations of the ground state structures of A and B are a must in order to find the free energy of each one (enthalpy and entropy). In case you do not run minimization to A or B you will have structures with higher energies, thus the equilibrium constant will be incorrect. Minimization of the ground state of A and B means finding the global minimum (GM) structures (the geometry with the lowest energy) of A and B. If you have the calculated energies of the GM of A and B the equilibrium constant estimated from those energies will be correct. In kinetics, if you have a reaction of X and Y to give P, and you do not do minimization to X, Y, P and any intermediate along the potential energy profile, the activation energy as well as the free energy of the system will be incorrect.
Summary: minimization is done (1) to find the global minimum structure for ground state structures such as reactants, intermediates and products. (2) To find the transition state along the reaction pathway. If minimization is NOT done, INCORRECT energies and geometries are imminent.