The purpose of neutral density filters is to decrease the amount of light that enters the camera. These filters have different density of filtration (1, 2, 3 stops). When you are looking to buy one, you will ask for either 0.3, 0.6, 0.9 or 2x, 4x, 8x. The technical process that happens when a neural filter is attached, is a slower shutter speed for a given aperture or, the other way around, a larger aperture on a given shutter speed. A good tip is combining this filter with a polarizer when shooting waterfalls.
The split neutral density filter (or gradual neutral density filter) is not coated in a uniform manner (gradually change from transparen’t to translucent gray); otherwise, it does the same this as above explained. These types of filters have a hard edge differing from a manufacture from another. The hard edge split neutral density filters can be used in difficult exposure situations when darkness and bright light are too close and the sensor cannot capture the entire range of values (a classic example is the time of sunrise). The use of this filter will make the light areas darker, reducing the exposure difference.