AH stands for Ampere/Hour, so basically a 10A/H battery could theoretically supply a load of 1 amp for ten hours, provided the piece of equipment was 100% efficient at converting its electrical supply to a mechanical or electronic load. (the perfect world)
here on planet earth, there are things called "losses', these can be all matter of things ( cheap pump bearings, poor fitting components causing friction, high and low ambient temps etc!) these can all effect how efficient the battery is at supplying the electrical load..another thing to remember is that a battery is not like a car, where a car can run full scream flat out until the fuel tank is emptied, a battery will supply its rated voltage for only a determined amount of time before the supply voltage is just below the rated voltage, this will cause the battery to operate at a lower voltage, but in order for it to still supply the load, the supply current will increase draining the battery quickly!
I work on a good estimate of 3/5ths, so that 10AH battery could supply a 1amp load comfortably for about 6 hours, but there is so many variables that also must be considered (cable size, connection quality, moisture, brand of battery, the list goes on)....
good luck