Grower is the skill for use with the Farming (Fields) labor, which allows a dwarf to plant seeds and farm plots, both above ground and underground. A high level of growing skill allows a dwarf to plant seeds at a faster rate, and seeds planted with higher skill will produce larger stacks of plants at harvest, increasing food output significantly. A single proficient grower can easily outproduce several dabbling ones.
A highly skilled grower not only increases raw food output, but also improves overall food production efficiency to a massive extent, since brewers, cooks, and threshers perform tasks with a single stack at a time. This has the effect of a huge multiplier on several labors, and also of making storage more efficient. For example, to get 25 booze, brewing five stacks of plump helmet  requires five visits to farm plots to store those 5 1-stacks in stockpiles, five trips to haul them to the still, five trips to haul five barrels, five brewing tasks, and will make five separate "stacks" of dwarven wine  requiring five separate barrels stored on five separate tiles! And that doesn't include all the tasks involved in making and storing those extra barrels. On the other hand, a single stack of plump helmet  can be brewed all at once into the same amount of dwarven wine , using a single barrel, hauled away in one task, and stored on a single tile. High-skilled growers can potentially save over 20* trips/tasks per single plant product, making your fort significantly more efficient. The impact this has on your overall labour force and fortress cannot be over-emphasized.
- (* save a difference of 4 to harvest to stockpiles, 4 to haul to the still, 4 for hauling barrels, 4 brewing, 4 hauling booze = 20 tasks; and that doesn't include cutting and hauling the wood and then making and storing the 4 extra barrels per stack.)
All dwarves harvest
If you leave the "All Dwarves Harvest" option on (in the orders menu), all dwarves, even nobles and children, will harvest when needed and gain experience in Grower. Harvesting is not as important as planting, as the size of the stack harvested is not affected by the harvester's skill level. However, harvesting crops does give experience, and if other dwarves are harvesting, then your planters will not gain experience as quickly.
If you turn on "Only Farmers Harvest", a single dedicated Proficient Grower can easily handle all the farming needs of a young to middle-stage fortress, especially if the farm plots, kitchens, farmer's workshop, food storage (raw and prepared) and dining hall are all located close to each other - as they should be.
Note: If your setting is "Only Farmers Harvest" and your lone Grower dies, is injured or otherwise occupied, your other dwarves will not harvest the plants, and they will rot in the fields, leaving no seeds. If you see crops piling up in the plots, check your Grower(s), and possibly turn the option back on until you have resolved the problem.
Many starting builds include a grower, as farming is generally the most reliable and safest of food sources. Having a proficient grower can help produce food early on to keep your dwarves fed and to attract migrants.