A convergence line is a band of cloud that remains fairly stationary and can produce large amounts of rain across a relatively small area.
Showers are the type of weather that give us rain, sleet, snow or hail in an almost random fashion. They are a form of convective precipitation that occurs when air rises over land or sea, unlike cold, warm or occluded fronts (dynamic precipitation) that depend on different air masses colliding.
Sometimes showers form less randomly in lines or bands when winds blow from different directions and collide. This forces the air upwards, and if there is enough moisture, clouds form and give rain.
A common example of a convergence line occurs because of a sea breeze during warmer months of the year, but convergence lines can happen at any time.