A manager collects information from a team and abstracts it to upper management. Upper management can then use this info to understand what the organization is capable of.
It's also the manager's job to understand where the company is going, what the strategy is, and communicate this effectively to the grunts.
They also relay and filter out information between departments. They help engineers understand what sales (and clients) want, and sales to understand what the product is capable of.
They suss out flaws, normally with people. Sometimes engineers might not be willing to voice out concerns.
The engineers might also want more resources, whether it's an outside service, hardware, more manpower. The manager looks at this from a higher level and finds the best solution. They appeal for budget increases and extend deadlines.
And if you have a really skilled dev turned manager, their job is to mentor and train. This is possibly the most effective thing a manager can do.