You might be able to imagine it this way. Take one gallon (8 pounds) of water and put it on your stove. If the water it 60 degrees F. and you want to bring it to a boil (212 degrees F.) then you will need about 1,200 BTUs to do this.
All combustible materials have a BTU rating. For instance, propane has about 15,000 BTUs per pound. Charcoal has about 9,000 BTUs per pound and wood (dry) has about 7,000 BTUs per pound. This gives you an idea of how much fuel you'd need to, say, cook something.
When it comes to gas grills they all have a maximum BTU rating per hour. If you see a 35,000 BTU gas grill that means that that grill puts out 35,000 BTUs from all its main burners combined in one hour, or uses a little more than 2 pounds of propane an hour. While the BTU rating on a gas grill doesn't necessarily tell you how much heat it will produce, it does give you a general idea of its heat output, and it tells you how much fuel you'll be burning.