Empathy has allowed me to adopt a broader perspective of the world. It provides a wider range of insights than could be gleaned from personal experience. Empathy is essential for both personal and professional success. Without empathy, I would be incapable of truly understanding what others are trying to communicate.
Empathy helps you to design software that can better address the client's needs. If you do not pay attention to what the client is asking for, you could deliver a product that (while techinically functional) does not satisfy their unique requirements. More than just listening, it's important to try to put yourself in the mindset of the client. What would you want if you were in their shoes? Clients are not always adept at communicating their needs. It falls upon an empathetic developer to fill in those gaps.