No one can explain to you what BTU is better than Wikipedia. So we will give you the wording from this popular and respected portal. So: "The British thermal unit (BTU or Btu) is a unit of heat; it is defined as the amount of heat required to raise the temperature of one pound of water by one degree Fahrenheit. It is also part of the United States customary units. Heat is now known to be equivalent to energy. The modern SI unit for heat and energy is the joule (J); one BTU equals about 1,055 J (varying within the range 1,054–1,060 J depending on the specific definition; see below). While units of heat are often supplanted by energy units in scientific work, they are still used in some fields. For example, in the United States the price of natural gas is quoted in dollars per the amount of natural gas that would give 1 million BTUs of heat energy if burned." However, we note from ourselves that the same method is used to measure room cooling.
Obviously, a smaller room or house with less length and width requires fewer BTUs for cooling/heating. However, volume is a more accurate measurement than area to determine BTU consumption because ceiling height is included in the equation; each three-dimensional cubic square foot of space requires a certain amount of BTU for cooling/heating. The smaller the volume, the less BTU's required for cooling or heating.