Airspeed in a nutshell
There are three airspeeds you care about....
1) Indicated airspeed (IAS) -- Think of this as how hard the wind would push back your arm if you stuck it out the window. Or, (oversimplified) how many air molecules per second are hitting the front of the airplane, times how hard they are hitting it. Higher altitudes and/warmer air = less air density (fewer air molecules per cubic foot of air) and so, at a given true airspeed, IAS is lower as you go higher or the air gets warmer. Most of the "normal" aerodynamic stuff -- drag, lift, response to the controls, etc. depends upon IAS. Stall speed, maneuvering speed, most "V" speeds are IAS.
2) True airspeed (TAS) -- actually how fast you are moving through the air. Think of it as how long it takes after the nose passes a given air molecule, for the tail to pass it. Some aerodynamic phenomena, most particularly flutter -- are dependent upon TAS rather than IAS, and so there will be limits -- Vne is TAS, for example.
3) Mach number -- how fast you are moving through the air relative to the speed of sound under those density / temperature conditions. Aerodynamic phenomena related to the compressibility of the air -- for example, how far back from the leading edge of the airfoil a shock wave forms -- are related to Mach number. Practically speaking, at lower altitudes a normal commercial aircraft is not going to be capable of getting anywhere close to the Mach limits, but at higher altitudes Mach limitations come into play.