The colour of light is determined by its wavelength, and because different wavelengths travel at different speeds when they pass through a lens, a phenomenon called dispersion occurs. As a result, the focal points of various colours do not all fall in the exact same focal plane. In a camera, this causes the focal point of some colours to be slightly in front of the image sensor, and the focal point of other colours to be slightly behind it (longitudinal colour aberration). In addition, different wavelengths are affected by magnification differently, causing the focal point to be offset to the right or left of the optical axis (lateral colour aberration).
Together, these aberrations can distort colour in captured images and cause unwanted colour "fringing" at the border between light and dark areas of an image.
To minimize the effect of the longitudinal chromatic aberration, which shows up as purple or greenish blurring in the defocused areas it is recommended to stop down the lens 1 or 2 stops. Using the lens with the aperture fully opened up will increase the likeliness of colour fringing.
As the effect differs with the shooting condition you can also try to change the focal length, the focus distance, or the composition to avoid the effect.
The lateral chromatic aberration occurs when different colours coming from an angle are focused at the same plane but at different positions, and it appears as opposing dual fringing (cyan/magenta, blue/yellow) and is more pronounced at the corners of the frame.
Unlike to the longitudinal chromatic aberration however, stopping down the lens does not eliminate these kind of colour fringes.
However most of the Sony interchangeable lens cameras (SLT, NEX, ILCE) can compensate this effect on supported Sony system lenses automatically to a certain degree. Make sure that the option Lens Compensation - Chromatic Aberration is set to AUTO in the camera or setup-menu of the camera. Refer to the manual for details on the specific camera.