In addition to all the good answers previously given, a conductor interprets what the composer has written. And different conductors may create very different interpretations of the same piece. They can set the basic tempo faster or slower, they can get the orchestra to really lean in to a particular musical phrase or de-emphasise it, they can bring out the horns at one point or hush them a bit and let us focus on the oboe or piccolo… A good conductor has studied and notated the entire score for some time before they and the orchestra even begin to rehearse.

So, part of that bow at the end can be to say, “what do you think of this interpretation compared to all the other times you’ve heard this famous symphony?” Then they usually turn around and wave the orchestra members to stand, which means, “and didn’t these guys do a great job executing it!?”