Hello SIRAISI,

Usually we use "the society" if we are talking about a specific club or
organization, as "The Society for the Prevention of Cruelty to Animals."

We can use "a society" if we haven’t yet specified which organization we
intend to discuss, or if we are talking about forming an organization.

We also use "society" without a determiner to mean people in general, or
the people within a specific cultural group.  We also use it to mean
economically well-off people who have a different lifestyle from the
rest of us.

Lastly, "a society" is used to mean "a cultural group". This is the
sense in which it is used in the sentence you have as an example,

Sincerely,
Jean Waldman, lecturer
Professional Writing Program, University of Maryland