1700 refers to the amount of energy that the battery stores. Think of it as the number of gallons in a fuel tank. It is 1700mAH, or milliAmpHours or 1.7AmpHours. It means that you can, give or take a bit, pull 1.7 Amps for one hour.
When you start drawing higher currents, you need to consider whether the battery is designed to deliver the higher current. In general, if your battery looks like it is made of "C" sixe cells, no problem. If it looks like it was made of "AA" or smaller cells, there might be some extra thinking needed.