I'll start by saying an electrical engineer type such as Romano will probably laugh at how I'm going to explain this, but I'm going to give it to you in simple layman's terms that are practical for how you use your RC cars.
"C" is a letter value given to equal the battery's capacity rated in amps meaning that 1C is equal to the capacity. "C rating" is the total amount of amperage the battery can put out based on it's capacity.
To calculate or understand a "C rating" you first need to convert the battery capacity from milliamps (mah) to amps which is really simple, you just at a decimal point. So it goes like this... a 5000mah battery is 5 amps, a 4600mah battery is 4.6 amps, a 4200mah battery is 4.2A... and so on. The amp number you just got is a "C"... so for a 5000mah battery, 1C = 5A.
Now the "C rating" is the "C-number" multiplied by the amperage. So using our 5000mah example again... if it has a 25C rating with a 40C burst, it means that the battery can safely put out 125A (25 x 5A = 125A) of power continuous (25C) and 200A burst (40C) - burst meaning a quick 5 to 10second surge of power like accelerating from a dead stop.
This goes for charging also. What they mean by saying you can charge your battery at 2C means you can charge at twice the capacity. So for a 5000mah battery, you can safely charge at 10A.
The problem is that marketing has caused people to put way to much emphasis on "C" ratings. People are paying big money for batteries with a 60C or 65C rating. Do you realize how much power and heat that puts out?!?!? If a 5000mah battery can put out 65C, that would be 325A which would more than likely melt the ESC, wires, solder, and/or connectors. Even the hard core drag racers aren't pulling more than 200 or so amps, so that means the average racer and basher are NEVER going to pull that many amps.
When buying lipos, make sure you stick with a quality brand. I don't mean high dollar, just a name that you know people use successfully with no problems. Stick to about the 5000mah range, give or take a couple hundred mah's and a 25C to 30C rating is more than adequate. Save your money and avoid the hype of the 45, 50, 60 C batteries. If you want to buy batteries locally, the Dynamite brand batteries are a good value. They are good quality and fair priced. If you want to order online and wait for a while, you can try some of the Turnegy and Zippy batteries from Hobby King. Many people use them with no problems, however while I worked at Randy's I saw several failures where the solder connections come loose, or the cells puff up and in a couple cases a brand new battery was below voltage and completely dead. There are many other brands out there, just ask around... but remember you don't need a super high C rating, it's just a waste of money. However, I would not recommend Venom batteries. I really don't trust them. I've personally seen some bad things happen with them.
LiPo ratings can certainly be more in depth with a lot more information out there, but that's the basics of it in a nutshell. I hope that helps and I'm sorry to be so long winded but "C" ratings confuse a lot of people so I just wanted to try and give a good explanation.