What is CAS and EAS and how to calculate from IAS?
If you don´t mind, I´ll keep it in simple terms.

We start off with IAS - that´s the airspeed you see on your instruments. You have static port - registering pressure around your aircraft, pitot tube, registering how many molecules of air getting inside. And by subtracting one from another, you get your IAS.
Dummy example: Static registers 100 molecules around. Pitot registers 200 molecules, which would equal to speed of 100kts.

CAS - it the speed corrected for instrument error. Because no instruments are perfect. 
Again, just one example, since a/c is moving through the air, pushing the air aside, it does create lower pressure around the a/c. Which in term, does affect reading of static and pitot tubes (registering wrong amount of molecules).
As a pilot, CAS is less relevant speed, as it will be used mostly for certification process.

CAS - EAS is made by allowing for compressibility effects. At very high altitude and very high speeds (jet fighters/bombers/space shuttle), there are different rules in action.

There is another speed, TAS. If you want to do everything perfect, first you need to convert IAS to CAS, (by using special table for a given airplane) and then convert CAS to TAS.
TAS is your real airspeed, moving through the air. It might differ greatly from IAS depending on pressure and temperature. In standard (ISA) conditions CAS will be equal to TAS.
But what happens when you fly at an altitude of 40.000 feet? Well, air is a lot less dense. For a given cube of air, there are a lot less molecules. 
In order to fly and not to stall, you must see "100kts IAS" on your airspeed indicator. Ssince there are so fewer molecules in the air, your real airspeed through the air must be 2-3 times higher, in order to hit all those 100 molecules. Does it make sense?

As a pilot, greatest importance for you is IAS. It shows you how many molecules of air you are hitting (dynamic pressure). Stall speed, never exceed - all based on IAS. Your TAS can be whatever, but IAS is the one affects your airplane.

So why do we care about TAS? Well, based on TAS and wind, we can derive our GS - ground speed. And GS is important! It will tell you, how long time will it take for you to get from A to B. Based on time, you know how much fuel you will need. Perhaps, you would need to make an extra refuelling stop on your way. Or you calculate and see that airport will be closed by the time you arrive there?
Later on, as an airline pilot, you know if you are early/late, duty times, etc, etc.

There is Mach number as well, but since you didn´t ask, I´ll just say you will need it flying at higher altitudes (approx. above 25,000 feet) and at those altitudes, it will take over IAS.