In a gathering profession the player harvests a type of resource directly from the environment. This resource can either be sold as is or processed by the gatherer into a new resource and then sold. For example, a Farmer harvests wheat and can either sell the wheat or create flour from the wheat and sell the flour. The focus of the gathering professions is to produce ingredients which are used in the crafting professions. (The Alchemist is the only gatherer profession that can produce an item which is directly usable by players, namely potions.) Practicing a gathering profession requires almost no expense, so is a good first profession for a new player. The gathering professions are: Alchemist, Farmer, Fisherman, Hunter, Lumberjack, and Miner.
In a crafting profession the player, following learned recipes, creates an item which can either be equipped or consumed. In fact, the vast majority of equipment and consumables that you will run across during the game were crafted by other players. A crafter requires a variety of ingredients, and this can make a crafting profession expensive to practice. Most players will, either in the same character or in different characters, practice a gathering profession that directly supports their crafting profession (like a Lumberjack and a Bow Carver). But notice that the Tailor and Shoemaker professions have a number of recipes that consist entirely of drops, so these crafting professions can be less expensive to practice if the player is willing to "harvest" these ingredients directly (i.e. defeating the appropriate monsters in the hopes of getting the appropriate drops). The crafting professions can be grouped as follows: