It's a relatively new career path. It's certainly the latest career term in Silicon Valley and the tech world. To be clear there are many companies that have confusing job titles and mean different things to different industries.
In the Banking and Finance world, the product managers they hire are sometimes related to those that management specific credit or lines of business "financial" products such as credit cards or loans.
Some banks still use this term for hire which is why searching for "Product Manager" on most job sites can be confusing as times (I know it has been for me).
Digital product management, mobile product management are really what we are talking about. Product managers and this role has been around since computers began really, but no one really talked about that because no one had a ubiquitous term back then.
Today, product management is concerned with any product (or equivalent) service that is sold or has users that use it.
Example of products could be:
These are just some examples of the types of products/service requirements management.
Product management involves the holistic understanding of knowing how the product can be made, what should be done to get the product to market and also what problems this product/service is trying to solve.
The intersection of this understanding and knowledge makes product management a multi-disciplinary career.
Sometimes people call Product Managers as Product Owners in certain settings. This is a discussion for another blogpost.