Say for example I have a TV with "140 watts" marked on it. Does this mean the TV consumes 140W per minute? Per hour? Per day? How is the power consumed by device calculated from the device specification?
If a car is travelling at 40 mph it doesn't mean it travels at 40 mph per minute.
If a TV is consuming 140 watts it means it consumes 140 joules per second.
What you get charged for by your utility company is joules and that is oddly (but acceptably) converted (without mathematical error) to watt seconds or more conveniently watt hours or kilowatt hours.
Maybe that is what confused you?
A watt is a joule per second.
It is a measure of power.
A joule is a measure of energy.
To calculate power consumed by an electrical device for a specified amount of time you multiply the power by the time.
You rarely if ever see things represented in watts per unit time.
See more: at this wikipedia link
If you want to calculate the amount of energy consumed by your device in a certain amount of time, multiply the power rating of your device by the period of usage.
For example: If you have a 100W lamp that is operational 24 hours for a full month, how much energy does it consume? How is that useful?
First, for energy consumption
Q =Power * time = 100 * 24(hours a day) * 30(days a month)= 72000 Wh (Watt-hour) = 72 kWh (kilo Watt hour) a month Which is a measure of energy.
Now how is this useful? You can see how much do you pay for it in a month. You will have to see first how much does the company cost you for kWh?