By wide-angle lenses we mean anything with a shorter focal length than 50 mm.
They range from ultra wide-angles of about 17mm to a more conventional 35mm. The latter is probably the most common focal length found on digicams. Its angle of view is 63 degrees, which makes it convenient for general photography.
Wide-angles are the obvious choice for landscapes, but they are also ideal for use in confined spaces where you can't go back far enough to capture the whole of the scene.
Wide-angles offer large depth of field, which makes focusing less critical.
One of the key things about wide-angles is the way they open up perspective.
Things that are close to the lens appear large in the frame while things further away seem to stretch out into the distance. The wider the lens the greater this effect.
This opening up of perspective can also introduce distortion. If you tilt the camera back when photographing buildings for instance, vertical lines will start to converge, giving the impression that the building is falling backwards.
Because you can get so much of a scene in, careful attention should be paid to composition to avoid creating “empty” photographs. Include some foreground interest to create a sense of depth and scale.