I struggle to answer this question sometimes as there are so many different ways to answer it. One of the simplest answer that I’ve seen is to simply state that I’m like the CEO for a given product. For most people, that answer only leads to more questions and a whole lot of confusion.
ScaledAgile.com, one of my favorite resources, defines a product owner as a member of the agile team responsible for defining stories and prioritizing the backlog while maintaining the the conceptual and technical of the features or components for the team. Which for a normal person, could be more confusing than the former.
To make things more simple, I like to define what a product is first. For the sake of simplicity, a product can be easily defined as anything that a team or individual is making iterations of progress towards a goal. This can be anything from a phone app, a website, a database, or a traditional product like the phone or device itself.
Now that we know what a product is, I can finally tell you what I do. My job is to write and prioritize the stories (or tasks) that will progress the product towards their goals. I am also usually responsible for setting, reporting, and communicating those goals and their progress.