Tveriah was a walled city when Yehoshua led the conquest of Eretz Yisrael. As such the reading of the Megillah should take place on the15th day of Adar.
There is a problem, however, which was raised by our Sages (Mesechta Megillah 5b). Although the city had walls on three sides, the fourth unwalled side faced Lake Kinneret. The question was whether the definition of a walled city was that it was completely blocked from the vision of outsiders, which would disqualify Tveriah, or whether it was protected from invaders, which would fit Tveriah as well.
Because of this unresolved question the Megillah was read in Tveriah on both the 14th and 15th days of Adar.