Professions in Neverwinter are a "click and wait" game, similar to the duty officer system in Star Trek Online or the companion crew skill system in SWTOR. Your character doesn't do anything herself, she just sends out her minions and reaps the rewards after a few hours.
The thing that feels weird to me is how your "minions" in this case are just really generic items that sit in your crafting inventory and can be traded on the auction house. At least the duty officers in STO have names and personalities, and it makes sense for a starship to have a large roster. As for why my half-elf cleric and my tiefling rogue have random guys doing all their work for them... who knows.
Professions are also really grindy. While levelling my cleric I focused pretty much exclusively on leadership, while ignoring all the other professions. Yet after two and a half months of playing and logging in every day, her profession level is still only 16 of 20.
The profession system is also one of the areas of the game where spending real money will give you huge advantages. Special workers who can cut a mission's time in half are only available from random packs that you buy for real money, while training up the basic white quality workers that offer no speed bonuses takes literally days and weeks of time.
While leadership at least is a very useful profession to have (I don't really have enough experience with any of the others to judge them), it does have a strong pay-to-win flavour to it that can be somewhat discouraging if you get a chance to compare your progress to that of someone who paid real money to gain advantages.