Product manager responsibilities
There are multiple responsibilities to a product manager. I'm going to go through some of them because the ideal product manager is a T shaped individual, with deep knowledge in one field and multiple experiences in other fields. An ideal product manager should have experienced every role in the PDLC (Product development life cycle).
Strategy and vision
A first key responsibility is about strategy. Strategy needs to be clearly articulated to the product team so they understand the intent behind the new product or iteration. The "why" needs to be supported with data and results from the customer development phase.
The strategy must also make mid or long term sense to the business goals of the company.
To be more specific, the product manager needs to make sure stakeholders, the product team, sales and marketing understands what is going to be built, what the customer value is, what pain is it solving and who the product is for.
After the "what" is articulated and support is granted (I always think that the first responsibility is a pitch to secure funding and support. This second responsibility is having a plan that makes sense) and vision is set, it's time to create an execution plan. This will include high level features and experience mapping for the customer journey to solving their pain.
After the high level features have been prioritized, the team tries their best to estimate them so a timeline can be created. This timeline will usually be rejected by stakeholders :). In a truly agile environment the roadmap will change and the team should always be working on the most important customer value it can deliver. In a waterfall environment, specifications change slowly.
The product manager is responsible for the groomed backlog, granular features and user stories and making sure the team is not stuck and requirements are clear on what needs to be built. The product manager is the glue between design, engineering and product and he/she has to ensure that there are no gaps and the team is able to deliver on expectations.
It's also important to deliver a minimum viable product (MVP) at first so the product manager can start asking for feedback from initial customers, stakeholders etc.
Launch and iteration releases
After the product has passes quality control, the value proposition has been validated by test customers, the product or feature is launched. This is where the product manager needs to start gathering quantitative feedback and decide what goes in the next iteration. Basically there will be a lot of decisions on what not to build.
If things go at least half of how they're expected to go, the product usually needs to enter a growth phase, reach maturity and a stabilization phase (months to years).