The shared meaning follows the sense number when there is more than one sense and the part-of-speech label when there is only one sense. It is a meaning shared equally by the entry word and the other members of the synonym group. This shared meaning is the "thing" that is referred to when we say that two or more words "mean the same thing" and thus are synonyms.
Sometimes there are words in parentheses within a shared meaning:
Entry Word: district
Text: an area (as of a city) set apart for some purpose or having some special feature <Independence Hall in Philadelphia's historic district>
Synonyms: neighborhood, quarter, section
Related Words: belt, zone; department, . . .
In the shared meaning at district, the words in parentheses indicate that district, neighborhood, quarter, and section are synonyms when they refer to an area of a city or something like that, and that the words in the related words list also refer specifically to this type of area.
See Verbs for information regarding the use and purpose of parentheses around certain words in entries for verbs.