A calorie is a measure of energy. If you've done any physics, you probably won't recall using it much - you would have used more common units like the joule. 'Calorie' as an energy unit is quite outdated... in every field barring nutrition.
When physicists coined term 'calorie', they defined it as the amount of energy required to raise the temperature of 1 gram of water by 1° Celsius (which is roughly 1.8° Fahrenheit). However, in a truly baffling turn of events, when dietitians (and sometimes physiologists) use the term, they actually mean a kilocalorie, or 1000 calories. This latter use has caught on, and so when we talk of a soft drink can containing 140 calories, we actually mean it contains 140 kilocalories (or 140 000 of the physicist's calories). Sometimes, this dietitian's calorie is written with a capital letter ("Calorie") to help distinguish the two uses of the word... but mostly it isn't. In this sense then, a Calorie is the amount of energy required to raise the temperature of 1 kilogram of water by 1° Celsius.
How Things Work have a nice little theoretical demonstration of what is means to talk of calories, and it's worth quoting it here:
If we look at the nutritional label on the back of a packet of maple-and-brown-sugar oatmeal, we find that it has 160 calories. This means that if we were to pour this oatmeal into a dish, set the oatmeal on fire and get it to burn completely (which is actually pretty tricky), the reaction would produce 160 kilocalories (remember: food calories are kilocalories) -- enough energy to raise the temperature of 160 kilograms of water 1 degree Celsius.
As you probably know, there are 3 major nutritional biological macromolecules: carbohydrates, fats and proteins. A gram of protein contains 4 kilocalories (4 Calories) of energy. So does a carbohydrate. Fats are different though - a gram of fat contains 9 kilocalories (9 Calories) of energy.
This helps to show why the body's chief long-term energy stores are fat - you get to store the most energy for the least weight (and in the smallest amount of space).