LiPo batteries are usually described as something like "5S2P 4200 maH 10C". This can be a bit confusing to understand.
The xSxP parameter descdribes describes the arrangement of cells in the battery pack.
The "5S2P 4200 maH" means there are 5 batteries in series, with 2 sets of these in parallel for a total of 10 cells. The capacity of the entire pack is 4200 maH and there are two sets of batteries in parallel, so the capacity of each individual cell is 2100 maH.
Alternatively, you can think of the battery pack as each cell is doubled up in parallel, then 5 of these doubled cells are connected in series. Either way, the pack will behave identically.
Imagine a jug which holds one gallon. If you drain this jug at one gallon per hour, then the bottle will be empty in one hour. If you drain the jug at half a gallon per hour, the jug will be empty in two hours, and if you drain the jug at two gallons per hour, then the jug will be empty in half an hour.
Similarly, a 2100 maH battery can supply 2100 ma of current for one hour, or 1050 ma of current for two hours, or other combinations.
Lipo batteries do not need to be fully discharged at the end of a flying day.
Each battery has an internal resistance which determines the maximum continuous discharge rate.
For NiCad/NiMH batteries, the internal resistance is measured in milliohms. The lower the reistance (milliohms), the more current the battery can supply.
A good rule of thumb is to estimate the maximum discharge capacity at 125 divided by the milliohms of internal resistance. For example, the Sanyo RC2400 cells which have about 4.5 milliohms of internal resistance can supply about 125 / 4.5 or about 27 amps of continous discharge current.
For LiPo cells, the maximum discharge rate is usually given as a C-rating, such as 10C or 12C. In the RC world, the C-rating specifies the current rating as a mutiple of the battery capacity. So a 2100 maH battery pack would be able to supply 2100 ma * 10 or 21000 ma (21 amps) of current. Note that this 21 amps can be either a maximum continous dicharge rate or a maximum burst discharge rate.
Note that reputable companies rate their cells conservatively for maximum current and their batteries will last hundreds of cycles at the maximum current rating. Less reputable companies will aggressively over-rate their cells, and if you continously draw the maximum current from the battery, it will only last for twenty or thirty charge/discharge cycles. Therefore, if you buy the cheapest batteries, you will spend more on batteries over the long term.