As an engineering-driven company, both daily tactical decisions and our overall strategic decisions are (usually!) based on technical data. This requires our management team to understand enough of the technical details in order to make sane decisions around product, forecasting, marketing, technical partnerships, etc.
It's important to note that I don't necessarily view the above tasks as more "important" than engineering. They're simply other business functions that need to happen for the business to work, and it's more efficient if I do it in my role rather than taking time away from actual development to provide the data we need for those functions.
Another function I serve on my team is technical tiebreaker. I work hand-in-hand with my tech lead, delegating most of the daily responsibilities to him, but when the team is mired in debate, I either cast a tiebreaker vote or if I don't know enough about $TOPIC, I can at least ask some questions to get them to consider the issue from different perspectives, which is enough to make progress in the debate..
Again, I note that the fulfilling the above job function doesn't mean I'm smarter than my tech lead (I'm not). But engineering isn't as black and white as we want it to be, and ofttimes we just need to make a decision, else the team wastes too much time bike-shedding.
A good manager is like a good IT guy. If he/she is doing the job properly, the team is only ever rarely aware of it. And that's just the way I like it.