Vasectomy reversal reconnects the pathway for the sperm to get into the semen. Most often, the cut ends of the vas are reattached. In some cases, the ends of the vas are joined to the epididymis. These surgeries can be done under a special microscope ("microsurgery"). When the tubes are joined, sperm can again flow through the urethra.
There are many reasons to undo a vasectomy. You might remarry after a breakup or have a change of heart. Or you might want to start a family over after the loss of a loved one.