Neutral density filters or ND filters for short are without a doubt one of the most critical accessories used when photographing the landscape, so much so it is not uncommon for me to carry anywhere between 4 and 10 of them with me at any given time.
Neutral density filters are essentially grey coloured filters that reduce the amount of the light entering the camera, there is a vast array of neutral density filters out there and they can be broken down into two main categories, graduated and solid.
Graduated neutral density filters are usually square filters that are half clear and half neutral density with a smooth transition across the centre of the filter. These filters are designed for landscape photographers and help to balance a bright sky against a darker foreground.
They are especially useful when photographing sunrise and sunset where you will often have a bright sky and a shaded foreground. These graduated filters are available in various different strengths which control how much they reduce the light by, the most common strengths are 1 stop, 2 stop or 3 stop although depending on the manufacturer these can be expressed as 2x, 4x, 8x for Cokin and Kood and 0.3, 0.6, 0.9 for Lee and Hitech. Not only are graduated filters available in different strengths but some manufacturers offer a choice how quickly the neutral density part of the filter becomes clear. The harder the line the harder the change from dark to light on the photo.
In the example below you can see the effect of using a 2 stop graduated neutral density filter and how it has helped to hold back the sky detail.
Solid neutral density filters are just that, a solid filter that reduces the light equally across the whole photo. As with graduated neutral density filters these solid filters come in an array of different strengths and are available as either square filters for use in filter holders or circular screw in filters that attach straight on to the lens. These filters are available in a broader range of strengths than graduated filters typically from 1 stop to 10 stops. The purpose of these filters is to increase the exposure time which can lead to wonderful effects especially when photographing around water. If the required exposure was 1/30th of a second by using a 3 stop ND filter you would extend this to 1/4 of a second, a 6 stop ND filter would give you an exposure of 2 seconds and a 10 stop filter would give you an exposure of 30 seconds. 
The two photos above illustrate the effect of using a 10 stop filter to increase the shutter speed from a 1/15th of a second up to 60 seconds, the pier remains constant in both photos however in the long exposure on the right you can see the soft blurring effect of the sky and the sea.
For more explanation about Camera Lens Filter, read article about Camera Lens Filter: Detail explanation