My experience so far: the role is very broad, and the responsibilities are -very- different across companies and products. The specifics depend on many things, like maturity/size/culture of your company, pricing of your product, whether or not it is open source, etc.
On one side of the spectrum you have PMs who are very close to the development teams, and you might still be contributing code regularly. You might be a sort of architect who also makes sure documentation is in order and who handles user feedback/discussions. These PMs are typically "user-focused", in that they try to improve the product for the end user.
On the other side you have a much more market-focused role (MBA type) where you'll do market analysis, pricing, marketing, sales materials, etc. You might see the dev team once a week, or maybe only the engineering managers. These PMs are typically "customer-focused", so targeting the buyers of the product (who might not be the actual end-user, but for example a CIO, depending on your market).
In any case: age/wisdom/maturity matters, it is not a junior role. You will also be in a lot of meetings. You will be the face of the product and you need to enjoy interacting with people.
edit: added the sentences about "user-focused" vs "customer-focused".