Craftsmanship

Increases the amount of progress gained when using Basic/Standard Synthesis.

Control

Increases the amount of quality gained when using quality increasing actions. The higher quality is for a synthesis, the higher your odds of making a High-Quality version of the item is. (Using HQ materials while crafting will also boost quality prior to starting the craft. The more HQ mats used, the more the quality bar will be filled at the start.)

CP

Acts as MP for all crafting jobs. Gauge fills completely when you change to a crafting class and when you finish crafting an item. CP does not recover during synthesis unless a CP recovery skill was used. Allows use of special crafting skills. Skill effects include increasing durability of an item, increasing Control stat each time quality of an item is increased (to increase chance of HQ item), etc.

Gathering

Increases chance to successfully gather an item. Will also provide a bonus to certain gathering nodes with Tree/Stone Whisperer.

Perception

Increases HQ gathering rate. Will also provide a bonus to certain gathering nodes with Tree/Stone Whisperer.

GP

Acts as MP for Miner/Botanist. Recharges by 5 GP every 3 seconds while not gathering. While gathering, each successful gather provides a static 5 GP.

Strength

Increases HQ chance for Blacksmith's Primary tool and Armorer's Secondary tool. Increases Botanist's Gathering.

Dexterity

Increases HQ chance for Goldsmith/Weaver's Primary tool and Carpenter's Secondary tool. Increases Fisher's Gathering.

Vitality

Increases HQ chance for Carpenter/Armorer/Leatherworker's Primary tool. Increases Miner's Gathering.

Intelligence

Increases HQ chance for Alchemist's Primary tool and Goldsmith/Leatherworker's Secondary tool. Increases Botanist's Gathering.

Mind

Increases HQ chance for Culinarian's Primary tool and Blacksmith/Weaver's Secondary tool. Increases Miner's Gathering.

Piety

Increases HQ chance for Alchemist/Culinarian's Secondary tool. Increases Fisher's Gathering.

Some information pulled from this thread, other pieces pulled from Gamer Escape's wiki.