This is an interesting phenomenon that almost everyone who’s ever watched an orchestra Conductor has likely noticed. It’s actually been discussed quite a bit among classical musicians and music aficionados. There are several reasons this happens. First off, the conductor must let the musicians know in advance what is going to happen. Secondly, in a large hall, there is a slight delay in what the audience hears based on the speed of sound coming from the stage (think of the “doppler effect”).
Especially when you have a large group of musicians playing together, the conductor needs to “pull” them along, so they will tend to make signals and downbeats just a brief moment before the orchestra actually plays the notes indicated in the score. With a chorus or choir of many singers, they will give an upbeat (motion upwards with hand/baton) to signal they should take a breath before singing. The conductor will also indicate changes in dynamics (intensity, often thought of as “loud” and “soft”) slightly ahead of when it’s supposed to happen in the music. Musicians like the conductor to prepare them for what’s coming next.
Check out this video of Beethoven’s Symphony No. 5, which clearly shows Conductor Masato Usuki seeming to be ahead of the orchestra with his movements: