When referring to chemicals, neat means a full-concentration, undiluted state. Neat chemical is rarely used directly in a process, and is almost always diluted first, usually with water.
The advantage to buying neat chemical is a huge savings in shipping and storage costs. For example, a 0.5% concentration of flocculent† might be needed for a setting tank application. Shipping the diluted chemical would use 200 times as much space as the neat chemical! Since water is conveniently piped right into our homes and businesses by the city and is available on demand, it would be much more convenient to store the neat chemical and dilute it as needed.
Typically, neat chemical is used in such small amounts that it is very difficult to meter it into a process accurately. Neat chemical might also be highly caustic, or difficult to dissolve into the process, or require special handling, or have other problems. In other words, it is usually easier to work with in a diluted state.
Dilution is often achieved with a mixing tank that adds a small amount of neat chemical from the storage tote to a large amount of water, and may have an agitator to perform the mixing. When the mixing tank begins to run low, more water and neat chemical are added. A large storage tote might be good for dozens or even hundreds of batches of diluted chemical.
† a chemical that helps to pull small, light particles in a colloidal suspension together to form large, heavy clumps so that they precipitate to the bottom.