Want to be a better product manager? Hone your leadership skills.
As much as I think of leadership, I generally don't equate it to what I do as a Product Manager. I think of my role as a leader to motivate people to do the right things (which sometimes is counter to my product, which is ok), to motivate others to think about their careers in different (better) ways, and to provide leadership on customer-focused products and how customers think. Funny that I usually don't consciously think about how leadership affects my outcomes as a Product Manager. I say usually because it does occur to me from time to time.
One benefit of being a strong leader as a Product Manager is the increase in productivity you can accomplish with your product. While product managers are generally skilled enough to cover all aspects of their product - marketing, business development, support, product development, design, etc - where's the productivity in that? No, better to have others pulling for you and stepping up to deliver functionality... hence making your product better without having to lengthen the calendar time to achieve such functionality.
I am releasing a product this month, and I am amazed at members on my team are saying to me "don't do that... I'll do it." Designers. QA Managers. Tech writers. Software Developers. Program Managers. Business Development Managers. They are all pushing the product forward, without me even asking them to. Wow. More than making me feel great, it is all about delivering more to your customers... and that's what it's all about, isn't it?