There relevant units are:
Watt (Power): Is the rate at which
energy is used, like miles/hour or the amount of wax a candle burns in a certain period of time. This unit describes the energy per time, not the energy itself.
Volt (Voltage | Spannung in german): Is the difference in electric potential. Similar to a difference in height between two volumes of
water, or gas pressure. "The higher the better", but too high gets dangerous and more difficult to handle.
Ampere (Current): Is the flow rate of electrons. Like gallons/hour.
If you multiply 1 Volt and 1 Ampere, you get 1 Watt. Both parts are needed to produce something useful. The water has to flow and there has to be pressure.
The next ingredient is time. 1 Watt * 1 hour = 1 Wh (
Watt-hour). This is a measure of energy. (The amount of wax burned.)
To the actual numbers: 156W = 1.42A * 110V
To get the time the motor will run, multiply 1.42A with the hours it has to run. for 24h * 1.42A = 34Ah.
Now battery manufactures tend to use theoretical numbers, that when actually used, will kill the battery. So the number above has to multiplied with something between 2 and 4.
Motors are usually rated at their maximum capability, so the actual Power drawn by the motor depends on the load and is likely to be below 156W.
As Deb Rebel already pointed out, one major factor is the battery voltage. At 110V the current is 1.42A. At 12V it is 13A. 13A is covered by the normal cables uses for household power.
Are you using an inverter to get the 110V? If so, it will have losses (below 5% for the best ones, otherwise about 20%).