Compressibility factor is significant because it determines how far a gas is from it's ideal state, based on various factors. The compressibility factor is determined by the pressure, volume, temperature and number of moles in the gas.
A gas in its ideal state has a compressibility factor of exactly 1 unit. Real gases often deviate from an ideal compressibility factor due to variations in temperature and pressure. As pressure increases, the compressibility factor of a gas also increases. As temperature increases the compressibility factor of a gas decreases. Factors that have the highest net effect on the compressibility factor of a gas are high pressure states and low temperatures.