As a child and teenager I was a member of a symphony orchestra. In my more senior years I was lucky enough to perform internationally with them. The more experienced I became, the more the conductor began to have meaning. It is hard to explain, but they are the "project manager" if you like. Not that we couldn't produce a fine sound together as musicians, but the conductor managed to bring together all the talent to a single voice, if that makes sense.
They don't merely stand around waving a baton, they are the beating heart of a skilled orchestra. They really need to understand the feeling behind every note, every passage, every orchestral part. It is a difficult job and demands exceptional musical skill.
What you see on screen normally, is a bloke with grey hair, waving a baton. What isn't shown, is the thousands of hours practice where the conductor drills his vision into every single member of the orchestra. It's hard graft all around to get anything like a cohesive sound.
This is one of the reasons why, if you attend a concert by an amateur orchestra, particularly if you record it, it can sound out of tune and a bit messy. Not always, but mostly. Ever noticed a childs brass band sounds out of tune? Thats the reason. A good conductor can hear and correct those issues.
I always considered my conductor to be the grandfather of the orchestra, as such, head of the family. That perhaps puts it in perspective. We had musicians which were far more capable on their instrument than he would ever be, but he was a master of the overall sound.
