Customer development is, broadly speaking, the process of doing directed work to improve your understanding of your customer. We want to know about what problems they have, how they see and interact with those problems, and what their values are.
You can make some good guesses based on experience, but people will always surprise you. There's often a huge disconnect between how businesses conceptualize their products and their sales process, and what is actually happening from the customer's perspective.
By better understanding the customer's perspective, we hope to make better products, do more effective marketing, and in general begin to make more money while doing more rewarding work.