Hey, this is a lipo i bought from BG: http://www.banggood.com/Wholesale-Lion-Power-11_1V-2200mAh-25C-LiPo-Battery-BT688-p-65635.html

and this is the ESC i used for it: http://rcbazaar.com/products/806-avionic-20amp.aspx

Were these both compatible with each other? Pls tell.
Also, if this ESC operates b/w 20-25 Amp, how to know which Amp is the battery ?

As far as I know, a particular ESC is either compatible or non compatible with a particular motor and prop combo (depending on the amperage drawn by it) . The battery is also either compatible/ non compatible with the the voltage and amperage drawn by the combination. Also, the battery amperage will depend on the flight timings / run timings that you are looking for.

For example, with a particular model using a particular motor and prop combo, a 3S LiPo rated at 1100 mAh may provide a 5 minute flight. The same model when flown with a 3S LiPo rated at 2400 mAh, may provide a 15 minute flight (everything else remaining unchanged).

The mAh rating of a battery is like a reservoir of water. The motor + Prop + weight of model is like a pipe that is draining the reservoir. The ESC is almost like a stopcock or tap that is controlling the drainage of water. The faster the plane flies, the more the ESC 'opens up', and the faster the battery drains. I hope this makes sense. Powerful motor + Bigger Prop (Dia Size and Pitch) = Faster speed = faster drainage of battery (mAh). The ESC just serves to drive the motor faster or slower.

What do you want to use the battery and/or ESC for?

At the moment, your question does not make sense.

ESC is rated for compatibility with the number of cells of Lipo it supports. It will be rated as 1S, 2S, 2S-3S, 2S-5S, 2S-6S or may be more. Your is rated 2-4 cells lithium battery as per spec since yours is 3S 3 cell lipo so compatible.

As regards to current. 2200mah Lipo rated 1C rating can give you 2200ma or 2.2 Amps. Since your is rated up to 25C it can give up to 25x2.2 Amps i.e. 55 Amps. So it can give the Amps the ESC supports i.e. 20 Amps. So again Compatible. 

As for lipo battery ratings, I never accept them at face value.  I always assume they are overrated.  Conventional wisdom says never go past 80% of the what it says on the battery sticker regarding maximum amps.

For example, a brand new Turnigy 3s 2200 mAh lipo 20C theoritcally can push out 44 amps.  Perhaps it can on its first few cycles but the stress will shorten the battery life.

Brilliant idea by the manufacturers to state the maximum limits with the C rating.  The more batteries you wear out, the more batteries you will have to buy and the more batteries that Turnigy can sell. 

Absolutely.  If you want to have maximum cycles out of your Lipo it's good thinking to adhere to 80% max current and only very short bursts of max.

Further for a brand new Lipo 10 cycles of breaking in with only 50% of max current goes a long way in maintaining its long usage.

Look,
the battery can give u maximum current of 25C x 2200 mAH = 25 x 2.2 Amps = 55 Amps.
And your ESC current is 20A Max and 2A BEC, so maximum current may go up to 22A.
Battery Safety factor = 55/22 = 2, so u r safe.