Why Does Maximum Power Transfer Occur When Z1 Equals Z2 in a Series Circuit?

Hi guys, I'm totally confused on something maybe the other take it for granted as equation but I need to understand the concept behind and if there's an analogy for, really appreciated.
I'm not understanding why if I have source supply connected serial to Z1 and Z2 (impedances) respectively so if I want to get maximum power on Z2 from the source supply, then for this condition, we must satisfy z1=z2 .. why is that correct? I mean lets assume that I take z2 bigger than z1 then I get power on z2 more than z1, and if z2 smaller than z1 then I get power less than the power on z1, and because I want maximum power on z2, then z2 "I assume" must be bigger than z1 and not equal ... so how is that going that if z1=z2 then the power on z2 from the power of the supply is maximum?! thanks alot

See if you can make sense of  thisCheers,Richard

Ryan for once you have asked a practical question and one that confused me for a long time as well.I think you are confusing Power Transfer with Efficiency. At the point of maximum power transfer, as you can see, your efficiency is exactly 50%.  This is what you get from a basic audio amplifier, there are ways to better this but don't worry about them now.  I have given below a table of the figures in Richard Gabric's reference, with efficiency calculated as well.

RL (Ω)	I (amps)	P (watts)	Efficiency
0	4	0	0.00
5	3.3	55	0.17
10	2.8	78	0.28
15	2.5	93	0.37
20	2.2	97	0.44
25	2	100	0.50
30	1.8	97	0.54
40	1.5	94	0.63
60	1.2	83	0.69
100	0.8	64	0.80

But if you load resistance (Z2) is high compared to your source resistance (Z1), your efficiency goes up.  This is the case when you are powering something from a battery or a power supply, these have very low source resistance Z1 and are usually operated for maximum efficiency, not maximum power transfer.Maximum power transfer is more important at Audio and especially at Radio frequencies where the source and load impedances need to be matched for this and other reasons.

Well, I understand all your explanations, thanks to the both of you.
but ! may please explain why I need to pass maximum power to specific impedance(audio)? I mean what does that result to?! for example maybe at maximum power if transferred will lead to my audio to be more clear "implicitly - no noise" ?! 
All of my point, what maximum power transferred result to get at the end? what its advantage in real life?! maybe if I transfer maximum power will lead to longer time to my audio?!

OK, if you want to have a hifi system with 8 ohm speakers (the load or Z2), your amplifier needs to have a source impedance (Z1) of 8 ohms also, that way,  as per the table above, your will get maximum power going to your speaker. The same applies to a radio transmitter, it needs to ahve a source inpedance of 50 Ohms to deliver maximum power to the antenna.