What they refer to is how properties such as density and viscosity change when you pass through the critical point.
Say you have water initially at 25°C under one atmosphere pressure. You heat it up and, of course, it boils into steam at 100°C. During the boiling process the density and viscosity drop discontinuously from those values for the liquid to the values for the gas, but once you have formed steam any further changes become continuous and at a finite rate. That includes reaching the critical temperature of 374°C, which really isn't critical at all unless you are also at the critical pressure of 218 atmospheres.
So, now try the same experiment but with 218 atmospheres (ctitical) pressure so that the water "boils" at the critical temperature of 374°C. Now you find the density and viscosity decreasing continuously, with no apparent break due to any phase change. But, at precisely the critical point, those properties are momentarily dropping at an infinite rate, much like the cube root of a number dropping at an infinite rate when the number passes through zero. The critical point is the one point where you get this infinite rate of change within a single phase.