The CID Menu provides a few commands for manipulating CID keyed fonts. If the current font is a CID keyed font the menu also includes a list of all subfonts that make up this one. This menu is only available in the font view.
A CID keyed font is a postscript (or opentype) font designed to hold Chinese, Japanese and Korean characters efficiently. More accurately a CID font is a collection of several sub-fonts each with certain common features (one might hold all the latin letters, another all the kana, a third all the kanji). This allows font-wide hinting to be crafted for subsets of characters to which have something in common.
CID keyed fonts do not have an encoding built into the font, and the characters do not have names. Instead the font is associated with a character set and on each character set there are several character mappings defined. These mappings are similar to encodings but allow for a wider range of behaviors.
A CID is a character index and is used to look up glyph descriptions instead of character names in other types of fonts. Using a character set PfaEdit will often be able to map a CID to a unicode character name (but not always), so PfaEdit will give characters names when it can.
For more information see the section on CID keyed fonts on the font view page.