Exterior covariant derivative

The exterior covariant derivative is a way to measure how a mathematical object changes as we move around it. Imagine a curve in space made up of dots - we could measure the rate at which the curve changes by looking at how quickly the distance between two dots changes as we move along the curve. The exterior covariant derivative helps us do that. It takes two dots, moves them in different directions, and then measures the difference in how quickly the distance between them changes. That tells us how quickly the curve is changing as we move around it!