Chromatic aberration occurs when the lens focuses wavelengths (that is, colors) of light at slightly different points. It's more pronounced at the edges of the lens than in the center, and in wide-angle lenses and at focal lengths of 300 mm and longer. This aberration results in color fringing (see Figure 1 and Figure 2). You're more likely to see color fringing if the subject is against a bright background, and you can sometimes (although not always) reduce the fringing effect by stopping down.
Figure 1 This photo was taken with a Sigma 50–150 mm f2.8 lens.
Figure 2 A close look at the side of the church tower reveals red and green color fringing caused by chromatic aberrations within the lens.