About 'Amp Hours' and 'mAh'

1000mah is the same as 1.0 'Amp Hour', so a cell/pack that is rated at 3300mAh can also be referred to as 3.3Ah.
'Amp hour' ratings are used to describe how much power can be extracted from a battery system over a given timeframe.
So, for example, a 3 Ah battery pack will provide 1 amp continuously for 3 hours, or 3 amps continuously for 1 hour, and so on.
When selecting a battery pack, find out what kind of current (Amps) your application will be drawing, and select an appropriate battery pack.
Note that if you need additional runtime, you can always add an identical pack in parallel (positive to positive, negative to negative) to double your Amp Hour rating, yet keep the same voltage. Add as many packs in parallel as you need to get the Ah desired. Example: two 3000mAh 12V battery packs in parallel will produce 6000mAh @12V.
Hooking up multiple battery packs in series (one cell/pack's positive to another's negative, then use the remaining positive and negative for your load), multiplies the voltage, but the overall Ah stays the same. Example: two 3000mAh 12V battery packs in series will produce 3000mAh @24V.

About 'C' ratings

“C” is a 1000:1 ratio of the capacity of a cell or pack in mAh to a given current in Amps.
For example, if a 1500mAh battery is rated to be able to have a max discharge of 10 C, that means the battery is capable of about 15 Amp max discharge (1500 / 1000 * 10 = 15)
Likewise, if a 4160mAh battery pack is rated at 14C max, you divide 4160 by 1000 (4.16), then multiply by the given 'C' (14C) to get 58.2 amps, which this particular pack is capable of.
To convert given amps discharge to 'C', do just the reverse: Say a given 4000mAh pack is rated at 48 amps continuous. 4000 / 1000 = 4. Then take the 48 amps divided by 4 , means this pack is capable of 12C continuous.
The same applies to charging rates as well as discharging.