wildbill:
I would actually say, from reading the OP's message, that they are misunderstanding how current works (your explanation though is helpful): They seem to be in effect asking "I have a battery that supplies 'N' amps, can I use it to power the Arduino without blowing it up? How much current can I supply the Arduino?"
This question, though, is wrong.
You don't supply current - you draw it. A battery (or a generator, or etc) -sources- current; devices you connect to it -sink- current. Those devices will only sink a certain amount; you need to ensure that the battery can -source- that amount.
For instance, let's say at max the Arduino -sinks- 1 amp of current, and you have a battery that can source 200 amps (perhaps a car battery); you won't blow up the Arduino with that battery (although the voltage regulator is gonna get mighty warm!) - it will only ever draw that maximum 1 amp.
Now - let's say you had something, like a motor, that could sink 1 amp of current, and you hooked it up to the Arduino directly (don't do this!); in this case, the Arduino is -now- the current -source-; since an individual pin can only supply about 40 mA of current (and really, you should keep it much lower than this) - that pin will blow, because you are trying to draw 25 times that amount from it!
This can happen to batteries and other components too (often with a loud explosion and/or fire taking place); for instance, a direct short across a D-sized alkaline cell can cause many amps to try to flow - and the battery will likely explode or rupture in fairly short time (if it doesn't vent properly first).