The role of the captain is one of those beautifully vague elements that TM is overladen with. 

The manual states that "Your captain should preferably be a player with a leader-personality, high professionalism (yes, it is a hidden skill), relatively low aggression and lots of routine."  However it desists from explaining just what having a good captain can do for your side and what the four elements that comprise the captaincy actually affect.

For example, if you have a candiate with leadership, professionalism, but no routine.  Or a player with loads of routine, low aggression, but no professionalism - who is better for the role?  And what if any, do each of these attributes impact upon?

I ran a thread on the international forum a while ago looking for some answers but received nothing conclusive.  Theories abound however.  What is certain is that occasionally the match engine asks can <your captain> rouse his troops.  This normally results in an attack for your team and perhaps the leadership or captaincy potential of the player in question affects the outcome of this play.  Similarly when the ME states that <your captain> tries to organise the defence.

Other theories (and just theories, by the way) are that your captain can influence how many cards you receive and your team's ability to come from behind, so to speak.  One guy reckoned that the captain's position on the pitch (and if he is a good captain, obviously) dictates the frequency you get defensive or offensive 'captaincy' plays in the ME.

Whatever.  The best advice is to scout your team and select the player with the best leadership to be captain and hopefully his professionalism and aggression are to standard (whatever it is that they do).  In the early days none of your players will have routine, so plumping for a youngster to fill the role is probably advisable.

Gotta love it.