The Gigafactory is the name given to what will be the largest factory producing rechargeable battery cells and packs in the world.
Tesla electric cars require large numbers of individual rechargeable batteries, known as cells. The cells (c.7000 in the case of Model S) are arranged together to form the battery pack. The production rate of Model S has from day one been supply constrained, largely due to the demands for these cells.
When Model 3 is released in 2017-2018, the demand for these cells will outstrip the current total world manufacturing capability.
In order to meet the forecast demand, Tesla, in partnership with Panasonic, the State of Nevada, and other suppliers is building a new cell and pack production facility whose capacity will exceed the combined output of every other battery factory in the world.
Image (c) Tesla Motors. Taken from http://www.teslamotors.com/sites/default/files/blog_attachments/gigafactory.pdf