With convergence you have depth perception and experience the world in 3D. The brain automatically fuse the image from your left eye and right eye together into a three dimensional image.

Lack of convergence or stereo vision usually does not affect reading but may affect ballgames and other sports where it is important to judge distance. People with monovision using only one eye generally develop alternate ways of judging distance......

It is believed that stereoscopic vision is developed by 4 months of age and will be fully established around 8 years of age. Generally it is assumed that the visual system is fully developed around the age of 8 years.

Severe convergence problems develop when one of the eyes turn in as in esotropia or when one of the eyes turn out as is the case in exotropia. This condition is known as strabismus. When the image from one eye cross the midline of the retina the brain suspend the image from that eye in order to avoid double vision. You may not even be aware of this before you are tested.

Slight convergence errors are often part of peoples vision problems. The blur may not be due to near-sight but rather to the fact that the eyes actually converge a little before the object you are looking at causing the image to be slightly blurred. If the eyes converge in front of the object viewed you will experience a slight doubling of vision. The same will be the case if your eyes are converging slightly behind the object you are viewing.

To illustrate this phenomena try this experiment. Hold up a pen or a finger in front of you. When you look at the pen/finger the background will be blurred and appear double. When you look at something at a distance you will see a blurred image of two fingers in the foreground. Looking at the near object your eyes converge on the pen/finger and the background will be beyond your point of convergence so it will appear double. Normally our attention is on the object of interest and we hardly notice the background.