Im no electrician but like I said above, Ive been digging around for some time now and Ill see if I can put some things in perspective.
-mah rating (as in 2200mah) is miliamp hour and is similar to a gas tank on a car, the higher the number (2200mah is more than 2000mah) theoretically the longer your flight times should be.
-"C" rating, as in 15C, 18C, 20C is how many amps the battery is capable of delivering, think of it as octane rating kinda. C is nothing but a designation for a unit of power, in this case C=however many miliamps your battery is rated. So, a 1C rating on a 2200mah battery would be capable of delivering 2200mah (2.2amps) sustained, or if a 4800mah battery had a 2C rating, it would capable of delivering 9600mah (9.6amps) sustained. A more relevant example would be a cellpro 2100mah 18C battery. 2100mah x 18=37800mah(37.8 amps) sustained. Amps are what your motor uses to create power and torque to turn the rotor and more amps=less bogging.
-lipos come in lots of flavors, the most relevant for a Trex being 11.1v and 2000+ mah and 15C+. For general hovering, forward flight, sport flying, etc. a 15C 2000-2200 mah battery should be lots of fun. 20C in the same 2000-2200mah configuration would be great for 3D and 25C (expensive and only a few manufacturers make them) would best be suited to a serious 3D rig running an insane motor and who could care less about flight time (5min or less).

This is not even scratching the surface but for the most part it lets you know kinda what to look for in a battery. Price, manufacturer, charging options, etc. all play their part as well. Also, batteries, motors, pinions, and Tx mixing/setup are all very much intertwined. It makes little sense to run a 2000mah 15C battery with a new JGF 500th motor turning a 13t pinion with big carbon blades and expect stellar performance. Matching things up seems to be the name of the game. You might be able to get a feel for performance from various configurations by reading the reports found on [link=http://www.trextuning.com/lipos.php]this[/link] paage, its by no means everything but its a start