Keeping that in mind the objectives vary pretty broadly. Perhaps the most important thing to keep in mind is that product management is NOT project management. Your goal is to deliver product success in order to hit a revenue target. That said product quality and product exposure are more important than release timelines, which is perhaps opposite of a project management role.
To really understand product management you must understand what drives user behavior in the choice and usage of your product versus the competition. Research helps a lot, but you still always find yourself surprised by the behavior of your users. Your assumptions of your users' behavior is probably often flawed.