What is the significance of Tu B'Shvat? How was it celebrated through history, and was it celebrated through history? What are the Halachic torah sources for Celebrating it? Why the recent Popularity?
Tu B'Shvat appears first in Mishnayos Rosh HaShana as one of the four Rosh HaShanas. The first of Shevat is the new year for trees, according to Bais Shamai, however according to Bais Hillel the fifteenth of Shevat. Fruit trees use Tu Bishvat as the cut off date in the Hebrew calendar for calculating the age of a fruit bearing tree. The Halachos of Orlah remain to this very day in the same form it had in talmudic times and uses Tu B'Shvat in the same way.
In the 16th century, the Arizal instituted that on Tu Bishvat we eat fruits from trees of Eretz Yisrael. By the Chassidim, some pickle or candy the Esrog from Sukkos and eat it on Tu Bishvat. Some pray that they will be worthy of a beautiful Esrog on the following Sukkos.
also see this link for more information http://www.chabad.org/kabbalah/article_cdo/aid/379846/jewish/Tu-BShevat-Basics.htm
@mevqesh and @user6591
The “Tu B’Shevat Seder” actually predates the Chemdat HaYamim.
The earliest written mention of the Tu B’Shevat seder comes from a sefer that was first published three years before the Chemdat HaYamim, in 1728 called Birkat Eliyahu by Rabbi Eliyahu of Ulyanov.
Rabbi Eliyahu cites his contemporary, Rabbi Moshe Hagiz of Yerushayalim, regarding a Tu B’Shevat Seder.
There, Rabbi Hagiz clearly states that he himself instituted this custom, based on the words of his Rebbeim: Rabbi Hagiz’ first Rebbe was his father, Rabbi Yakov Hagiz of Morocco zt”l. Following his father’s early death, Rabbi Hagiz studied with his maternal grandfather, Rabbi Moshe “Magen” Galante, zt”l whose own grandfather, Rabbi Moshe Galante of Tzfat zt”l was a Talmid of the Arizal
This shows a clear chain of tradition from the Arizal down to Rabbi Moshe Hagiz, who first spoke of a "Tu B’Shevat Seder" and formally established it.
Here are the words of Rabbi Hagiz, as quoted by Birkat Eliyahu (page 55):
…as it is written,” כִּ֤י הָֽאָדָם֙ עֵ֣ץ הַשָּׂדֶ֔ה - man is a tree of the field” [Devarim-Parshat Shoftim 20:19], and so I established a custom, based on what I have seen from my rabbis, and my teacher [Rabbi Moshe Galante] who, on Tu B’Shevat, would customarily recite many blessings on fruits and pray to Hashem to renew for us a good year. And they would eat these fifteen fruits…
Hope this helps.