Leonard Bernstein conducting, from The Enjoyment of Music
I recently attended a symphony concert with two Indians for whom it was the first time at such an event. At intermission they asked me a question that I expected, and which gets asked by Indians quite often. “But what do they have conductors for? Can’t they all just sing or play their instruments all by themselves?” I later related this to an American friend and his raised eyebrows were exactly the response I expected from that quarter.
It’s a hilarious question at some level, but I have to say that the conductor does occupy a strange place. For western people, who have always seen them, they are part of the musical scene, no questions asked. They are as normal within the setup and as critical to it as, say, the violins. But to an Indian, the first time they see an orchestra or choir, the main thing they wonder about is, “What’s up with all that waving of hands and batons?”
Some Indian music basics:
Choirs and large orchestras do occur in Indian film or popular music, but not often and almost always behind the scenes. So their conductors, and I assume they do have some, are invisible, and are likely to be the composers themselves, at least when the original (and often the only) recording is made. There is no tradition of printed music scores in Indian popular music, and Indian classical music relies heavily on improvisation, and thus is even further away from printed scores. When there is an ensemble of musicians (i.e. orchestra) on stage, it is almost always in support of a soloist (or two). The soloist may be a singer, or an instrumentalist but the critical point is this — the ensemble takes all the cues from the soloist. Changes of tempo and other performance details all originate from the soloist. In this sense, the soloist is the conductor, but in an implicit fashion.
It seems to me that the main reason it has evolved in this way is that Indian music is melody-centric and soloist-centric. Certainly, in Indian classical music, there is the main performer, or sometimes two main performers (in a jugalbandi for example), who the paying public have come to hear. The others may get to shine for a small part of the concert, and often get thanked and praised by the soloists at the end, but it is always clear who the lynchpin is.
While the soloist’s creativity is central to a performance of classical Indian music, the main goal of any live performance of Indian popular music is to reproduce the sound of the original recording as closely as possible, rather than to (re-)interpret it. More importantly, in popular Indian music, the main tune is where all the action is and everything else is a supporting act. In this genre, melody is king. 
The contrast with Western (classical) music:
Contrast this with western classical music. For almost a thousand years now, polyphony has been an integral part of this soundscape. The melody or theme may dominate for a few measures here and there, but will get harmonised quickly and variations too will soon appear. The melody will often get passed around from one instrument to another, thus creating an egalitarian balance among the parts. The chordal and key structures give the music texture and emotion, rather than a single line of melody, and because no one instrument (or voice part) is more important than the rest, you need an external entity to keep it all together. Enter the conductor.
The primary reason, and originally the only one, for the waving of arms and batons was to keep time. Indicating the beat so that the ensemble remained in sync was the conductors main job, and often, the conductor was also an orchestra member. Over time it became the norm to have an external conductor, and the duties of the conductor also expanded. He (and it is most often a he) started to become an interpreter of the composer’s music — tuning the dynamics and tempo and cuing various musicians to be louder or softer during the performance so as to bring out the intent of the composer as he saw it.
A conductor today is often called the director or artistic director of the group. This means that he chooses the music, maybe even the musicians and soloists (perhaps through an audition process), works with the group in rehearsals, and may even decide upon the performance venue, thus creating an orchestra or choir with his own imprint.
Stories about conductors abound as well. The most famous, and tragically hilarious one, is that of Jean Baptiste Lully. Back when the baton was not the standard device for conducting, he used a heavy staff to conduct, and it landed on his own foot. Gangrene set it, he refused to have it amputated, and then died when the gangrene spread. Another common story, perhaps apocryphal, told about many conductors, including, as I recently found out, an Indian one, is about the ability to listen closely, and point out to one member of, say, a 50-strong violin section and comment, “You were flat on measure 108.” This conductor of legend often has entire symphonies memorized as well, and uses no score.
There are times when a conductor and his choir or orchestra become a single unit. They learn each other’s methods perfectly over time, and the positive feedback between them creates an energy that lights up massive concert halls, even energizing the audience. And there are times when there is no chemistry. Orchestras are known to hate the occasional guest conductor, often for seemingly trivial reasons, and give him a hard time. In fact, in my choral experience, there was a director we worked with on and off, and most of us found him so rude that we never sang as well as we could for him.
Yet other times, choirs (and, I assume, orchestras too) just ignore the director. This is often unintentional. They may not look up from the music often enough, and one of the sections may speed up or lag behind. Or they may autonomously decide to disobey some creative decision made by the conductor. I remember a performance of Messiah in which our director had decided to do Hallelujah a little differently from normal. She wanted to build up the excitement gradually rather than have us burst out from the get-go. Well, it turned out the choir had a mind of its own. I mean come on, it was the Hallelujah chorus after all, and we just wanted to go for it. She gave in and let us have our way at least for that one night. That was great!
Of course, there are groups without conductors. Some (e.g. Chanticleer, some chamber orchestras) may have a director during rehearsal, but not while performing, others (e.g. many string quartets, the King’s singers) do everything by consensus and don’t have a conductor even for rehearsals.
For groups that have a director, on the face of it, it may seem that the director directs, and the others merely obey, but it is more complex than that. Without a willing orchestra or choir, there is nobody to direct, and no music to create. Directors too learn and adapt over time, developing their personal methods. No method works all the time, and no method works for all groups. Both sides need the other, influence the other and, unsurprisingly, a mutual sense of belonging, even of ownership, builds over time. There is a give and take, a negotiation, an offer, a counter-offer, a compromise, a halfway point and finally, hopefully, a meeting ground that all go into the creation of sound. Somewhere in that constant exchange lies the true essence of conducting.
 Some of these characteristics are shared by western popular music. Soloistic features — melodies, complex rhythms for one instrument at a time — are an important part of this genre and stand out during performances. The singer is often the most famous member of the band, though the rest of the ensemble isn’t nearly as auxiliary as in the case of Indian music — guitarists and drummers, in particular, are often as big as the lead vocalists. Harmonies, key changes and chordal structures do play a role, but soloistic features dominate.