It's a trick that allows us to use the equations of ideal gasses for real gasses. Real gasses are a lot more complicated to work with but it turns out they "behave the same as" an ideal gas at a different pressure (meaning they have the same molar Gibbs energy and temperature). That's the fugacity: the pressure an ideal gas would have to be at to "behave the same as" your real gas.

For example: Let's say you have a real gas with a fugacity coefficient of 1.2 at a pressure of 1 bar. Then you could either use some complicated formulas for real gasses or you could use the same old equations for ideal gasses but instead of the actual pressure (1 bar) you use the fugacity (1.2×1 bar= 1.2 bar) and you will get the same result.

Side note: sometimes fugacity is defined to be unitless, sometimes people give it units of pressure.