The equilibrium of two molecular conformations is determined by the difference in Gibbs free energy of the two conformations.  From this energy difference, the equilibrium constant for the two conformations can be determined.
If there is a decrease in Gibbs free energy from one state to another, this transformation is spontaneous and the lower energy state is more stable.  A highly strained, higher energy molecular conformation will spontaneously convert to the lower energy molecular conformation.
Enthalpy and entropy are related to Gibbs free energy through the equation (at a constant temperature):
Enthalpy is typically the more important thermodynamic function for determining a more stable molecular conformation. While there are different types of strain, the strain energy associated with all of them is due to the weakening of bonds within the molecule.  Since enthalpy is usually more important, entropy can often be ignored. This isn't always the case; if the difference in enthalpy is small, entropy can have a larger effect on the equilibrium.  For example, n-butane has two possible conformations, anti and gauche.  The anti conformation is more stable by 0.9 kcal mol. We would expect that butane is roughly 82% anti and 18% gauche at room temperature.  However, there are two possible gauche conformations and only one anti conformation.  Therefore, entropy makes a contribution of 0.4 kcal in favor of the gauche conformation.  We find that the actual conformational distribution of butane is 70% anti and 30% gauche at room temperature.