Prevent other teams from reaching in and randomizing our priorities, work on promotion plans for anyone seeking promotion, manage customer/partner team relationships, ensure everyone has balanced feedback regularly, mediate disputes, collect information to manage upwards so we can still be funded, advise on team process but never mandate it, facilitate accommodations, manage poor performance so the team isn't dragged down, try to consolidate and clear meetings from calendars across the team.
If I'm not around, then all those things either don't get done or fall to the engineers themselves. I personally think it's useful to have someone on the team specialize in those activities for the benefit of the team. But I'll admit my bias.