Shulchan Aruch O.C. 553:2 states that eating on Erev Tisha B'av must end while it is still daylight.
In viewing the topic of tosefet Shabbat which is mentioned in Talmud Rosh Hashannah 9a, I understand why Shabbat and Yom Tov begin before nightfall.
The term used in the Talmud is מוסיפין מחול על קודש - "We add from the profane to the holy" or, in this case, we add time from the weekday to the holy Shabbat or Yom Tov.
Why would this apply to Tish'a B'av, though? What is the "holiness" in Tish'a B'Av? There is no prohibition of melacha as there is on Shabbat and Yom Tov.
Even more puzzling is that when Tish'a B'Av is observed on Sunday, as is this year, we still begin the fast before the end of Shabbat. That seems like we're doing the opposite by adding from the "profane" onto the "holy".