What we mean by the calorific content of food is actually quite vague. Calories used to be calculated by seeing how much energy was released when the food was burned in controlled conditions; the technique we currently use to estimate the calories for food labelling is instead to add up the calories we would expect from each nutrient group (carbohydrates, fats, proteins, etc.). Neither of these methods is truly an accurate estimate for how much energy our bodies are able to extract from a certain food.
Take, for example, wholegrain foods compared to refined, white flour. On first glance, wholegrain would appear to be more calorific, and this is what the food labels will say, too. But the calories in white flour and products made using it are readily available and easy to extract, whereas wholegrain foods have most of the usable calories locked up inside insoluble, difficult-to-digest cellulose. We have to actually expend a lot of energy to break down – both physically and chemically – some foods, while other foods are ready-to-go energy sources.
The same is true when applied to the banana.
Mashing the banana before eating it breaks the banana down physically, reducing the amount that you need to chew it. Chewing requires energy, so by mashing the banana you are saving energy and in effect maximising the number of calories you obtain from the banana. Mashing the banana will also release pectinase and other enzymes usually associated with fruit ripening from the banana cells, which start breaking down the big molecules in the fruit; long-chain carbohydrates are broken down into sugars, proteins are broken down into amino acids, etc. This will also minimise the amount of energy your body needs to use for the chemical breakdown of the banana, as this process is already partially complete.
For a banana, though, the difference in calorific content are likely to be insignificant as bananas are a soft food that requires very little chewing, and in a ripe banana most of the carbohydrate is already broken down into sugars, so don’t let this affect your banana-eating habits!
References and further reading:
How the calorie content of food is determined:
Why calorie counts are all wrong:
The fruit ripening process: