We see insulation all around us. Most mammals are covered in fur, which is one of nature's forms of insulation (blubber is another). When you go outside on a cold winter day, you put on a coat, which is fashionable insulation. As a general rule, the thicker the coat the more insulation it provides. Up in your attic you can probably see the insulation between the rafters.
All of these different forms of insulation are trying to prevent heat transfer. And there is a very good reason for the insulation in your home - it saves a LOT of money. Energy for heating and cooling is the biggest expense of owning a home on a day-to-day basis. During very hot summer months or very cold winter months, a home can use hundreds of dollars in energy. Insulation helps lower that bill by slowing down the movement of heat through the walls, floors and ceilings.
Insulation is measured by its R-value. The R-value lets you calculate how much heat will move through a certain wall area depending on the temperature difference between the indoor and the outdoor air.
So let's say you have a wall that contains R-10 insulation in the United States. Let's say the wall measures 8 feet high by 10 feet long, or 80 square feet. Let's say it is 70 degrees F indoors and 30 degrees F outdoors, or a 40 degree F temperature difference. The calculation looks like this:
80 square feet * 40 degree F difference / 10 = 320 BTUs
In other words, you would need a heater producing 320 BTUs to compensate for the heat loss through that wall, and that heater would be running continuously.
If you are not in the United States, you do the same kind of calculation but you do it in SI units, using degrees C, meters, square meters and SI R-values. What you get out is watts. So if you have a wall that is 2.4 meters high and 3 meters wide (7.2 square meters), and the outside temperature is -1 degrees C while the inside temperature is 21 degrees C (22 degrees C temperature difference), and the insulation is SI R-1.8, you get:
7.2 square meters * 22 degrees C difference / 1.8 = 88 watts
If you multiply watts by 3.4 you get approximate BTUs and vice-versa.
So now let's look at a house. Let's imagine an idealized 2,500 square foot single-story house. It is a square that has 4 walls that are each 50 feet long and 8 feet high. The ceiling and floor are 50 x 50 foot squares. The ceiling has R-30 insulation. The floor has R-15. The walls have R-10. It is 70 degrees F inside and 30 degrees outside. How much heat is escaping through the insulation?
Each wall is 50 x 8 = 400 square feet for a total of 1,600 square feet. With a 40 degree F temperature difference and R-10 insulation you get:
1,600 * 40 / 10 = 6,400 BTUs
The ceiling has 2,500 square feet at R-30, so:
2,500 * 40 / 30 = 3,330 BTUs
The floor has 2,500 square feet at R-15, so:
2,500 * 40 / 15 = 6,660 BTUs
So the whole house needs about 16,400 BTUs (or 4,820 watts) to maintain its temperature.
No real house is ideal like this, however. A real house has windows that might be at R-2. And doors that might be R-4. And there are little leaks that allow cold air infiltration, plus less insulation around outlets, etc. All in all, a real 2,500 square foot house might need 20,000 to 25,000 BTUs (depending on how many windows/doors and how "tight" it is) to maintain its temperature.
But when you go to buy a furnace, they will spec something much larger than that. They might use detailed calculations that look at the exact number/size of windows and doors you have, or they might use a general table like this:
I live in North Carolina, so it thinks I need 35 to 40 BTUs per square foot to heat the house. For a 2,500 square foot house that's about 87,000 to 100,000 BTUs. Why is that so much higher than the number we just calculated? For one thing, it can get down to -5 degrees F in North Carolina. And some people like to crank the heat up to 80 degrees F. So now the temperature difference between inside and outside is 85 degrees. That more than doubles the BTUs. And then you have some padding so the system isn't running constantly, plus some padding to handle heat loss in the ducts, etc.
This video offers a nice look at different ways to add insulation in the attic for better efficiency:
See also this video on furnace efficiency: