National Coaches or NC's as they are known are simply a coach of one of the many national teams in Trophy Manager (TM). It doesn't matter what country you are from, you can manage any National Team (NT) you want, so you don't have to be from Bolivia to be the NC of Bolivia, however it helps. Also to be an NC you don't just have to be in Division 1. You could be in Division 7, however the chances of you winning the election will be very slim as you won't have as much experience in the game compared to most of the other managers competing against you in the election.
If you are in a low Division and you do wish to get some NT experience under your belt then I suggest that you run for one of the less populated countries as it is easier for you to win those elections as very few people will be able to vote. However do expect a lot of competition for the post as there are hundreds of teams like you thinking just the same!
Once you become an NC you take charge of your NT for two seasons which gives you chance to take part within a major tournament. You go through qualification then if you pass that then you can put your skills up against some of the best NC's in the game.
If you win a trophy whilst you're the NC your club won't get anything directly but no doubt the respect earned from winning the honour will follow you around for ever!
NT Sales Edit
At the end of every season all NC coaches are encouraged to take part in the "NT sales". This is where all the players that are potential/NT quality who play for either banned/inactive teams will be saved and placed on the Transfer List (TL) for $100,000,000 and anyone can bid on them in order to keep the NT's as strong as possible.