What are CAS and EAS used for?
The different airspeeds:


IAS is indicated airpseed
CAS is calibrated airspeed
EAS is equivalent airspeed
TAS is true airspeed


CAS is IAS corrected for instrumentation and position errors. The errors are most pronounced in slow and high angle-of-attack flight.

IAS figures in aircraft manuals are actually converted from CAS. For ease of use.

How CAS is determined (Wikipedia link).



However, a modern plane with an air data computer (ADC) actually displays CAS, despite being labelled as IAS.

Below 200 knots and 10,000 feet, for all purposes, CAS equals EAS.

As the plane goes faster and higher and compresses the air, the air changes density, an effect known as compressibility that affects the CAS reading.



EAS is computed by the ADC on a modern fast plane, and together with the density altitude, the TAS is then known.

Ground speed and track (from GPS, navaids, and/or INS) together with the TAS allows the FMS to calculate and display the wind speed/direction.

Before ADC's, pilots used charts like those in the answer.

Summary:

In a modern plane, what the pilot actually uses is CAS, despite being labelled IAS. And EAS is used in computing the TAS by the ADC.

For engineers, TAS (actual velocity through the air) is used in lift equations, EAS is used in calculating dynamic pressures on the plane (TAS corrected for air density).



Source used and a must read: Aerospaceweb.org—Types of Airspeed