A conductor is a position in front of an orchestra that gives hand gestures to direct the performance of the music.
Maybe not quite as depicted above, but we tend to have a stereotype of a conductor who waves his arms ferociously, with a lot of passionate springy hair, and as a special effect, splashes his sweat all over the auditorium.
What does a conductor do? The job description of a conductor, besides the preparatory work of selecting and coming up with interpretation of a piece, on the stage also includes cueing and directing the beat, tempo, as well as the dynamics of music. But I argue that these are not really the most critical role functions played by a conductor.
Consider a soloist playing a single instrument. Does she need a conductor? No. She takes care of the preparatory work of selecting and interpreting the piece, and she takes full control of the performance on stage.
With an ensemble, a conductor may help with coordination, but the role is not critical. Dynamics of the music is typically written into the musical notation, and good musicians can play by ear and eye contact with each other to coordinate the cue and tempo. A conductor can walk off the stage, and the orchestra could still keep playing. So what really is the critical role of the conductor?
If you have played an instrument as part of an ensemble, you would know that you tend to hear your own part really well. You could definitely hear the other parts, but not in a way for you to tell how to adjust your own loudness so that the ensemble sounds good. The conductor is a few steps away from the ensemble, away from any particular instrument, so that he can hear all the parts as a whole.
His job is to make sure all the instrument parts come out well balanced. This is not something any individual musicians can do on the stage. The balancing of parts is even more critical the bigger the ensemble.
In other words, conducting is actually very similar to what a sound engineer does these days with a mixer. A sound engineer works with mic inputs across several channels, and each channel strip would allow changing the level and tone characteristics of each part electronically. The end goal is the same, to ensure that all the parts sound good in the mix.
A conductor, therefore, is a sound engineer before electronic mixing boards came about. Sound engineering needs an ear towards creating balanced sound. It is a delicate science. Having parts fighting each other in the same frequency spectrum causes hearing fatigue. To those who don't know the science of psychoacoustic perception, the science might appear as an art, but it's an art that can be explained with a scientific basis. Like how visual art is founded on science with color theory, perspective, and composition.
Knowing that creating a balanced ensemble sound is the critical function of the conductor, a good conductor would not only cue and direct the beat and tempo, he would make eye contact with the part that needs adjustment and ask the part be played louder or softer. It is imperative for ensemble members to follow his direction. After all, although he might seem like the authority figure, the ultimate goal of his leadership is to help individual instrumentalists archive one and the same end result, that is to deliver a great musical performance.