There are two main kinds of lenses: converging lenses and diverging lenses. Their names are very self-explanatory. When parallel light rays pass through a diverging lens, they emerge on the other side, spread out. A diverging lens is also known as a concave lens, because one or both of the sides is concave.
A converging lens makes parallel rays that pass through it converge at a single point, called the focal point, on the other side. It is also known as a convex lens.
As you may have noticed, in both these lens diagrams, the rays are only considered to refract in the middle of the lens. Though in reality this is not true, it makes everyones job easier in drawing optics diagrams.
Before going on to examine how lenses produce images, it is first necessary to get acquainted with certain optics terms. In the diagram above, the parallel rays going through a converging lens met at a focal point. In fact, all lenses have two focal points: one on each side of the lens. The focal point on the diverging lens was not so obvious in the diagrams, though it is located at the point the diverging rays appear to be coming from, on the first side of the lens. Lets look at a diagram of a lens in a more geometrical way.
The lens in this case has been reduced to a (blue) line, which, in three dimensions, represents the plane that cuts through the center of the lens. As you can see, each of the focal points lies a fixed distance from the lens, the length of which is known as the focal length. The reciprocal of a lens focal length (expressed in meters) is called its power. This quantifies how well a lens can make light beams converge, and is measured in dioptres (D). For instance, the power of a lens with focal length of 0.25 m is 4 dioptres. A converging lens always has a positive power, while a diverging lens, which does the opposite of making beams converge, has a negative power.
You may also notice that the focal points lie on a line which goes through the middle of the lens. This line is known as the principal axis, and is used in lens diagrams to determine what will happen to an image. Because the principal axis passes perpendicular to the lens, and through the center, any rays on it remains unchanged, and it is therefore used as a kind of point of reference in lens diagrams.