As of beta release 1.71, there are 15 different professions that can be assigned to your settlers to achieve different goals. They include:
Every settler can gain experience in a profession by completing tasks associated with that profession. (ex: Wood chopper: chopping wood, Blacksmith: smelting ingots)
As a settler gains experience in a profession, they gain levels in that profession. This lets your settlers work faster and craft new recipes.
Levels matter more for some professions than others. For example Carpenters and Blacksmiths have many high level crafting recipes (Lv. 10+) and Miners cannot mine ores below their skill level. However Farmers and Wood Choppers will work faster at higher levels but have far fewer crafting recipes with fairly low levels. This should be taken into consideration when assigning professions for your settlers.
Switching Professions Edit
A settler may be set to a different profession with no experience loss whatsoever. This comes in handy when starting a new game, and not having enough settlers to do all the different jobs you may need.
The unit list ('u' key) can be used to change professions while seeing other settlers experience levels and can be used to help optimise your settlement.
Planned Changes Edit
Professions are planned to change significantly in a future update with the inclusion of a independent skill system.
'...The basic idea is that villagers will have a profession, but what they level up will be skills. So, your forager, using his bow and arrow, will level up an archery skill. Which will be transferrable to archers. And a bunch of others.' - Ethrel, 2014