On Saturday evening there is a confusing practice to reverse the order of lighting the candles on Chanukah and Havdallah. Intuitively one would think we would recite Havdallah first, and then light the candles of Chanukah, after all we are lighting these candles for the next day.
Rabbi Moshe Soloveitchik suggests that any time we have a command to publicize a miracle there are two components of the command. The obligation of the individual and the obligation of the community.
Each evening when we light the candles of Chanukah at home we fulfill our obligations as individuals and when we light the candles in Synagogue we fulfill the obligation of the community.
Rabbi Chaim Soloveitchik (Rabbi Moshe's Father), suggested that this may be why we reverse the order of lighting on Saturday evening while in the Synagogue. Once the full Kaddish with the request Tiskabel (accept our prayers) has been recited, we are no longer a community unified by our objectives (i.e. beseeches G-d in prayer) but we now are standing as individuals having concluded the service.
If, indeed, we are obligated to light candles on Chanukah as a community, we must act as a community, be united as a community and be involved in the communal act of prayer when lighting the candles of Chanukah. Once we have uttered the requested Tiskabel, prayer is concluded and our community status is thus removed. This necessitates the counter-intuitive switching of the recital of Havdallah only once we have lit the lights of Chanukah.
All this being said, what remains as a significant point for further reflection is this idea of community. What brings us together? What separates us? What transformation takes place during the service that immediately ends with the final request for acceptance?