A Mach number is a ratio of the relative velocity of a flow of a fluid by an obstruction and the speed of sound in that fluid.
An Alfvén Mach number is such a ratio specifically with the speed of Alfvén waves. The term sonic Mach number is sometimes used for the usual Mach numbers to distinguish the two.
Both these Mach numbers are used in the study of the dynamics of molecular clouds and dense cores, to characterize turbulence according to the relative velocities of adjacent fluids. They are of interest in determining the affect of turbulence, jets, and winds on the stability of parcels of high-density gas, essentially to study the particulars of star formation feedback.