In a cathode-ray tube, the proper alignment of the horizontal and vertical lines, ensuring that they remain perfectly perpendicular to each other. Also in a CRT, convergence refers to the crossing over of the three separate electron beams (the red, green, and blue) at the plane of the aperture mask.
In networking, the term convergence refers to the process of synchronizing of a network after a routing change has taken place. Convergence time is the time required for all routers to be updated with new routing information.