I have seen people (mainly sefardim) put a few drops of water into the wine before havdallah. Why do they do this?
Probably to ensure it's not Pagum.
I.e.: If somebody already drank from that wine, it cannot be used for Kiddush or Havdala unless wine or water is added to it, as Paskened in Shulchan Aruch.
ו: יְכוֹלִין לְתַקֵּן כּוֹס פָּגוּם עַל יְדֵי שֶׁיּוֹסִיפוּ מְעַט יַיִן, וַאֲפִלּוּ עַל יְדֵי שֶׁיּוֹסִיפוּ עָלָיו מַיִם מִתַּקֵּן.
Some people always add some water, *just in case * somebody drank from the bottle and they didn't notice. I've seen Hasidim do it for Kiddush.
As wine used to be much stronger than today, drinking wine undiluted was considered bad manners. Oppositely, whereas at the time, wine could be very diluted and still be considered wine, we fear that dilution will remove its status as wine. Therefore, we add a few drops to not drink it undiluted, but also not risk losing its status.
Maybe it's because of this idea, seen on torah.org:
According to the "Kol Bo," "some have a tradition to draw water [from a well] Motzei Shabbos, because Miriam's Well supplies all the wells each Motzei Shabbos, and one who does so and drinks will be cured of illness" (Orach Chaim, 299:10)
See also the last paragraph of bais yosef 299.