Getting to know your target audience and what drives them and affects them is an important part of developing anything. Beyohd this, though, just coming up with software ideas relies on empathy as much as creativity. Using your own experiences is obviously a good starting point to brainstorm ways to improve certain aspects of technology, but it's so incredibly limiting. Being able to use others' experiences is what opens the windows to endless possibilities for improvement and innovation.
Being able to see where someone else's head is at in important in a collaborative setting. No two people work or think the exact same so the more you can try to relate and open your mind the more supportive that team becomes.
My most recent job I was managing a family of bars in Austin. One of the biggest things I've learned is that sometimes life happens and there are things you can't change. Sometimes people are just having a bad day or got stuck in traffic or had something terrible in their personal life happen. Being able to have empathy at those times has helped keep good employees around and build a team that had each others' backs. It also harbored honesty and personal responsibility.
You're never going to get along with every person in your life and in a professional setting it can get hard to empathize with someone who perhaps you don't click with and then added stress comes along. Being able to empathize on a professioal level is a must, as you can put aside differences to get to the root of the goal which is solving that problem or finishing that project.