What is the importance of Dimensionless numbers?

Dimensionless numbers allow you to compare two systems that are vastly different by combining the parameters of interest.

For example, the Reynolds number, Re = velocity * length / kinematic viscosity. If you are testing an airfoil with a particular Re, and you want to run a simulation on a scaled-down model (length is smaller), you could increase fluid velocity or lower kinematic viscosity (change fluids) or both to establish the same Re and ensure you are working under comparable circumstances.