Understand that I have absolutely no direct experience of this: I am judging by looking at the examples around us and how we see them acting in their roles.
Clearly one of the important roles is selecting a match-day 22 and setting up the strategy for each match. He's probably not alone in that role; there is a whole team of coaches and the like involved and they will probably have feedback into setting the strategy.
Another critical role in the last 22+ years is building towards each RWC. We can see in Australia and New Zealand two formerly great players: Smith and So'oialo reaching the end of their careers. Both sides seem to have found good replacements, possibly great ones. South Africa have done something a bit different with the Lions tour this summer - Smit amongst others has stayed when he might have otherwise retired to play against the Lions. You can never be sure with PdV but presumably there is some plan in there to replace those players and blood them next year in the Tri-Nations in preparation for 2011. The midweek matches on this November tour are probably the start of that.
Another role must be managing, to some extent, the players in the team and the players around the team. The young All Black lock, Donnelly, who played many Tri-Nations matches was told to stay at home and bulk up, get stronger. I'm sure he was disappointed, but it has let Boric come on tour and learn from that which is good from the squad's perspective and it has given him clear goals about what to do and what they want from him. Nothing wrong with that at all - coaches have to make these sorts of decisions and if the players understand them, then it's all good. Similarly it appears the Australian team and Robbie Deans had been butting heads but they sat down and trashed things out. Giteau was understandably disappointed to be passed over for captaincy but seemed in several interviews to understand the decision and to be mature enough to set aside his disappointment because he understands that the coach considers it to be better for the team. In one interview he quite clearly said he agreed it was probably the best choice for the team. That's all good.
Part of the former role must be being seen at the matches. Obviously there will be choices: you can't be at every match and for some coaches it's easier than others but planning a schedule where you get to see all the teams reasonably often and to spot talent has to be part of it. Saying to the players that aren't in consideration yet but might be next year that you, the coach, is aware of them and maybe saying "this is why you're not there yet" should be part of the game.
Then there is the dubious delight of interviews. The media, ex-players and others, all look for a bon mot. A reaction to the defeat or the victory. A comment about progress. Something that is fairly true but diplomatic and suitable for a tea-time family audience.
It has occurred to me, whilst writing this, that there's actually very little rugby knowledge needed. You'd need enough to have the ability to communicate well using the right words. Certainly the skills coaches, defence coach, scrum coach, backs coach etc. need to have the technical skills too and determining the best players in each side requires an interest and probably more technical knowledge than I think (I don't have the technical knowledge and experience but would like to think I can spot a good player at most positions). Graham Henry may or may not be the greatest coach in the world (he does have a stellar record and has kept his side right at the top of the world rankings for the last 6 years) and whilst he taught rugby, he was a teacher - someone used to communicating. OK, he has a rugby-mad population and great player base to choose from too but is it a coincidence I wonder?
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