There are plenty of definitions out there regarding the role of the software engineering manager, but the most accurate one I found is in Julie Zhuo’s book “The Making of a Manager”:

Your job, as a manager, is to get better outcomes from a group of people working together.

The definition can be well understood by imagining yourself operating a store as a single person. The business is going well, and you notice you are getting a lot of customers and looking to make more profit. Thus, you decide to hire more people to help you grow your business. Suddenly, you are responsible for a group of people (manager) to help you grow your business. If your people aren’t working well together (e.g. bad spirits, unclear responsibilities, unhealthy environment … etc) then you won’t be getting better outcomes.

This abstract definition pretty much sums up the role of a manager.