C rating is a strange unit because what it means depends on the mAh of the battery.
25C on a 500mAh battery means half the current of 25C on a 1000mAh battery.
To make it simple, 1C means that the fastest rate you're allowed to drain the battery is such that is completely drains in 1 hour. 2C means you can drain the battery twice in one hour, or once in 1/2 hour (of course you can only drain the battery once, then you have to charge it again.)
This means that a 30C battery can be drained in 2 minutes, and a 60C battery can be drained in 1 minute. The faster you drain the battery, the more power you are using. If you try to drain a LiPO battery faster than it's rated it will most likely destroy the battery. If you stay well below the C rating your battery will be able to be charged more times and will maintain it's mAh rating for a longer number of charges. It will still degrade but slower. C ratings therefor effect the longevity of the battery.
The length of your flights have nothing to do with the C rating unless you happen to be drawing more current than the C rating and mAh allow. In the case where you're drawing more current than rated, the battery will overheat and the internal resistance will increase and the voltage will drop and your helicopter will loose power before the power contained within the battery is used up and you'll have to wait for the battery to cool down before you can fly again (if you haven't destroyed the battery).
Anyway, 20C means the battery can be drained 20 times in 1 hour, or in 3 minutes. If you have a 1000mAh battery, then 1000mAh 20 times in 1 hour is 20,000mA or 20 Amps.
A 20C 500mAh battery can supply (20C*500mAh) 10,000mA or 10 Amps.
Let's say you have a helicopter that requires 10 amps to fly. You can use a 20C, 500mAh battery to fly for 3 minutes, or you can use a 10C 1000mAh battery to fly for 6 minutes. If you use a 20C 1000mAh battery you'll still only fly for 6 minutes even though the battery can supply 20 Amps because the helicopter won't draw 20 Amps. However, since you're using the battery at half it's rated capacity (10 Amps) it will last for more charges and will be less likely to overheat and get destroyed.