It's important to leave enough leaf, otherwise the grass will be spending resources constantly trying to re-generate itself to it's natural state. A healthy leaf is important because this is the mechanism by which the plant photosynthesizes. Cutting too short will cause your lawn to be in constant state of stress, therefore jeopardizing it's long-term health. The lawn may look fine when the weather cooperates, but if it gets hot and dry you'll find the lawn goes into stress very quickly. If you have a tendency to cut your lawn on the long side you can risk an overactive thatch layer.
Every lawn has a thatch layer.
It's the transition zone between the exposed plant and the roots. This provides the necessary function of converting spent grass material into a form of food that the roots can use. Sun and oxygen are needed to maintain a proper balance. If the grass is too long preventing these elements from reaching the layer, it can become host for disease. Keep your blade sharp.