At the end of each skill meter in the character's status box there is a box that you can click on to check it. Why would you want to check it??

...Because checking it means they are more likely to stay on that task and get better at it.

Also, they will (in most cases) choose to do that task without being told, say they are a doctor - they will heal people on their own.

It's just a useful little feature so that you don't have to watch the villagers every minute of the day to make sure they're working

You do need to train them a bit also, but once they have some training - checking the box of a particular skill will indeed cause them to 'prefer' that task.

They may still wander a bit, I've noticed when food is low they will farm a little no matter what the preference is, but the check helps them stay on task to gain skill and once they are masters in many skills, the check indicates what task they will mostly be performing.

And , when you quite the game (except if you put it in pause. and it's not advisable to stay in 2x speed), the best is to be sure that you have checked at least 2 doctors and 1 farmer (it depends of how many villagers you get) so your villagers will be healed and the food bin filled.