Convergence has to do with how different colors are displayed on a screen or monitor - typically the rear projection and some other types. When colors are overlapping to create unexpected combinations, or leave gaps between areas where overlapping is expected that results in a shifted red, green or blue image strip or edge - that is an indication of a convergence issue. They can look like this in severe cases:
Colors will drift, so manufacturers often include a utility to help you nudge the colors back in the right place. Most times this utility is buried in the Set Up Menu and when activated, produces a screen like this:
You will need to adjust the red, green and blue colors for each cross so that only a white cross is displayed. Keep red, green and blue fringing to a minimum. When you're done, the screen should look black and white, symmetrical and straight - like this:
Problems arise when you are no longer able to coax the utility to give you these crisp, B&W results with no red, blue or green ghosting. This is often due to a failing convergence integrated circuit ("Convergence IC"). Many times, replacing it will solve the problem, but other times it can be the result of failing components either ahead or after this IC. If you're attempting to replace this IC, please make sure the TV or monitor has been *unplugged* for 24 hours or more to allow the dangerously high voltages to dissipate.