Full text searching is the ability to search for any word, phrase, or combination of words. In the case of CartoType maps, that means looking up map objects based on their names or other string attributes.
The makemap tool for building CTM1 (map) files creates a full-text index by default. You can turn that off if you like using /textindex=no.
All the attributes of a map object are indexed except those with names starting with an underscore; such names are used for things like road speed limits, which shouldn't be found by text searches.
The full-text index is used by the address searching functions in the CartoType framework.