Refer to figure. 
Indicated Airspeed (IAS) is the airspeed indicated on the ASI. Calibrated airspeed (CAS) is IAS corrected for instrument and position error, if an aircraft has an air data computer this is what's displayed on the airspeed indication.

A basic ASI assumes that air is incompressible, but at higher speeds air entering the ASI pressure capsule becomes compressed causing it to over-read. Equivalent airspeed (EAS) is CAS corrected for compressibility error.

EAS is rarely used by pilots and V_MO is the only speed based on EAS. For navigation purposes we are interested in the actual speed of the aircraft through the air, this is called True Airspeed (TAS).

At sea level in ISA conditions EAS and TAS will be the same but as an aircraft climbs, and air density reduces, TAS will slowly increase if EAS remains constant. This is because an aircraft needs to travel faster to maintain the same expansion of the pressure capsule in the ASI (same EAS) as the density of the air gets less. TAS is EAS corrected for density error.

Note: An easy way to remember the errors affecting airspeed indications is the mnemonic ICE T Is Pretty Cool Drink as illustrated in the figure above.