<human>: Could you distill the essence of the text into 1-3 sentences?

I was pondering this a little while ago randomly, and then recently my girlfriend and I were given tickets to an orchestra here from her aunt.  It's not exactly my style of music, but I'm always down to check something out.

While watching I was trying to see what the conductor was really doing.  I think the idea is that they are leading the musicians and keeping them all together.  But what I couldn't help but think is that they'd be fine without him as well.  The musicians are of course all amazing at their instruments, and were looking at their sheet music 99% of the time.

Finally, the last piece had a singer come out, and the conductor was behind her, so she was taking literally zero queue from him, which furthered my idea that, for these professional musicians, they could do without the guy up front with the little wand.

Yet the conductor always gets top billing, and their names are always quite well known (at least in those circles), leading me to question my questioning.
<bot>: Really, what does the conductor do?  How important are they?  And if you took the same orchestra, and switched conductors would anyone notice?