Subsonic flow is a self-explanatory in that it is intended toward air speed that does not exceed the local speed of sound. This will be in velocity calculations for much consumer and ground travel; however, there are also high-speed transport vehicles (trains) in development. Typically, this is represented through a Mach number less than 1, or the flow velocity registered past a boundary.
Transonic flow is a bit of an oddity in the sonic spectrum, as it includes elements on both the sub- and supersonic flow regimes. Typically, the Mach number associated with transonic flow is between 0.8 and 1.2M. Although supersonic commercial flight is certainly a possibility being worked on in years to come, most commercial flights will occur within the transonic flow regime.
Probably, the most familiar concepts would be the wonderfully heroic ones of sonic boom and supersonic flow, where velocities in the flow regime are greater than the speed of sound (have a Mach number greater than 1). We model and simulate this through various boundary and curvature phenomenon; however, some examples of supersonic flow consist of jet propulsion and bullets.
We also think in terms of hypersonic flows; however, there is no accurate definition (or at least agreed upon consensus) of the value above a Mach number of 1, where velocity is differentiated between supersonic and hypersonic. Historically, hypersonics have had use and function within missile defense systems, spacecrafts, and rocket-powered planes or jets, but forward-thinking engineers might re-think the potential for hypersonic development.