In your first example, families is an array containing 3 strings.
['Droid Sans','Cookie','Parisienne']
In your second example, families is an array containing 1 string.
["'Droid Sans','Cookie','Parisienne'"]
To make this work, you want to do something like the following:
var fntstr = "'Droid Sans','Cookie','Parisienne'";
var fntarr = fntstr.split(',');
WebFont.load({
google: {
families: fntarr
}
});
The split method will split your string at each comma and create an array with the elements.