An object that is double gilded has two layers of gold leaf laid, one atop of the other. This is normally done with the traditional water gilding process and imparts a very deep, golden tone that is generally free from defects in the gilding. Water gilded leaf has a satin tone in its natural state; burnishing the gold or silver leaf brings the metal to a brilliant lustre.
When water gilded leaf is left satin, it's left un-burnished. This means that the leaf not only has a satin tone but is also not compressed against the wooden object, such as a picture frame, and therefore bonding of the leaf to the gessoed wood is somewhat more vulnerable to wear. It has historically always been this way and old gilded frames and furniture that has unburnished satin areas will likely show more wear than its burnished counterparts. Therefore, I often use additional RSG (glue) in the gilding water to aid in adhesion and sometimes apply a 5:1 RSG:Water wash over the satin leaf for added protection.
Single layer gilding usually results in some anomalies ('spots' exposing underlying clay bole from pin holes; air holes or breaks in the leaf) during the process of water gilding, many of which can be covered during spot gilding, although if done excessively the result can be unsightly. Double gilding covers all the anomalies that single gilding sometimes leaves behind and is useful when gilding satin areas. It offers a very solid layer of gold leaf.
There are times, though, that the somewhat translucent quality of single gilding is preferred when developing a satin section, especially when other areas of the gilded object are rubbed, abraded, or distressed. As an example, a picture frame that is antiqued to some degree can be somewhat jarring if the sides are a strong solid double gild. It is often aesthetically best if the overall appearance of the gilding presents a sympathetic quality between each of the sections, where no one area is dramatically different in its condition.