Explain why Silver chloride when kept in the open turns grey with a balanced chemical equation.

The reaction of silver chloride in the presence of sunlight is as follows:

$2AgCl\to 2Ag+C{l}_2\uparrow$

Because elemental silver, which is grey in color, is produced when silver chloride breaks down, the color of silver chloride changes from white to grey.
It is a type of photolytic decomposition reaction.