In electrical terms, you can think of power as the rate at which energy is converted.
W = I x V
Think of it this way, a 2W interior lamp in a vehicle is not as powerful as a 60W headlamp.
This means that that the 2W interior lamp will convert chemical energy in the battery into heatenergy at the lamp at a much slower rate than the 60W headlamp.
In other words, the 60W headlamp will flatten the battery much faster than the 2W interior lamp, because the headlamp is more powerful.