In an open type sight, the rear sight is merely a piece with a notch cut in the middle. The notch is typically V-shaped, square shaped or U-shaped. The front sight is usually some kind of ramp or post.
The above picture is an example of an open-type sight. It is typically made of steel or polymer. Note the rear sight is merely a small piece with a square notch in the center. The front sight is a small post type. In the above example, the front sight is fixed to the barrel, but the rear sight may be slid left or right using proper tools, to adjust the horizontal alignment of the sight. In the above example, the rear sight also has a white line surrounding the notch, to give it greater contrast from the surroundings, to make it easier to aim.
In some cases, the front and rear sights also have small dots of some material that glows in the dark (e.g.) glass tubes filled with tritium gas. This helps in picking up the sights in the dark as well.
These sights are characterized by their simplicity of design. There is not much that can go wrong with them. They are also small and unobtrusive, so they don't affect the balance of the pistol much at all. They also can't get caught easily on clothing or holsters because of their small size and shape. Hard blows may bend or move the sights out of alignment though, but on the whole they are pretty durable. Rain, fog and snow don't affect these sights much at all. These sights are cheap to manufacture and don't use batteries or electronics, so there is less to go wrong.
These sights are not as precise as other sights though. Square shaped notch on the rear sight provides the best accuracy of different open iron sight types. Other types are not as precise and also take longer to aim. Peering through the sights also obscures other details which are covered up by the sides of the sights.
Sights like these are pretty useful up to about 300 meters or so, though most average shooters can shoot them typically to 100 meters or so. These are therefore typically used by shorter range weapons such as civilian shotguns, police revolvers and pistols etc.
One famous assault rifle that was originally designed with open type sights is the AK-47. The rear sight is an adjustable one with a simple V-shaped notch cut on it, while the front sight is a post. The rear sight may be slid forwards and backwards to adjust for range. One may now purchase AK clones with other types of sights as well, but the original version was designed with open-type sights, which is typical for this simple, reliable weapon.