Conductors tend to look like they're just waving their arms if you've never worked with one... they have two primary functions, artistic and practical.
The artistic one often starts with choosing the repertoire, which is an art in itself. Picking music that will make a good programme and suits your orchestra and that you can reasonably expect to sell a hall-full of tickets for requires a lot of knowlege of repertoire, particularly if you're not just going to play the famous stuff. Then, having picked the pieces, the conductor will set the tempo, set the dynamics, and generally the way the piece is played will be the way the conductor hears it.
The practical stuff involves running rehearsals, answering every question the musicians can come up with. and often a degree of input into things like reheasal scheduling and administration, choosing and recruiting new players, working with soloists... In the arm-waving department, some of the primary things you need a conductor for are so you all start and finish at the same time, waving cues at people (I'm a piccolo player, you spend an awful lot of time counting sixty-bar rests to play a couple of quavers and losing count!), getting the time changes right and consistent... a lot of it's not so much about telling your musicians what to do as making sure they all do it in the same dynamic at the same time! Consistency to the conductor's vision of the piece is what matters.
It's like directing a play or film, you're not actually acting but you can see a good director's stamp all over any play they've worked with - like any Hitchcock film is immediately and obviously a Hitchcock regardless of the actors and the script, or any Spielberg action film is obviously a Spielberg. With practise you can make a reasonable stab at naming the conductor and orchestra in any recording.
It's also worth mentioning the differences between working with different sorts of orchestras - symphony (the big orchestral repertoire), sinfonia (smaller scale works), opera (specialising in accompanying singers), ballet (specialising in working with dancers), and so on. Opera and ballet conducting requires yet another set of skills because it's not just about conducting the orchestra, it's about getting them to play precisely the same every time, coming in with the dancers, conducting the singers on the stage as well as the orchestra in the pit, knowing what position the dancer has to be in before you can start the next piece... nightmare! And the orchestra can't do any of that for themselves in a theatre as they're underneath the stage and facing the wrong way...