Double quotes allow for interpolation whereas single quotes do not.
For example, using double quotes :echo "foo\nbar"
will output foo
and bar
on separate lines whereas :echo 'foo\nbar'
will not interpret \n
as a line break and will output foo\nbar
literally.
For more info on different types of quotes type :h 41.2
for the help file and read the part near the end of the section with the heading STRING VARIABLES AND CONSTANTS
.
This said, don't confuse quotes for strings with the double quote at the beginning of a line comment. Single quotes never start line comments, only double quotes do.