Tu B'Shevat is generally regarded as the "New Year for the trees," (Rosh Hashanah 2a). We are told that by the fifteenth day of Shevat most of the rains for the given year have already fallen (Rosh Hashana 14a). As a result, Chazal tell us that until this date all the fruits that grew are a product of the rains from the previous year, and the fruits produced from this day onward are from the rains of the new year. In fact, it is for this reason that many have the custom to pray for a beautiful and kosher etrog for the upcoming Succot holiday on this day (see Lashon Chachamim 1:38 of the Ben Ish Chai for a text of the prayer). Tu B'Shevat also bears halachic significance for the purposes of counting the years for orlah, terumot u'maaserot (tithes), and according to some opinions for determining the holiness of fruits that grow during the Shemitah year. It is for this reason that many communities have the custom to eat several different types of fruits as a means of celebrating the day (see Mishna Berura 131:31, Kaf Hachaim 131:97).
The halacha also states that we refrain from reciting tachanun on this day (Orach Chaim 131:6). This custom appears to be a bit puzzling since we generally refrain from saying tachanun because of some sort of happiness. On Tu B'Shevat, however, what is the nature of the day's happiness, since most of the rains have fallen due to purely natural means? In order to gain clarity of the significance of the day, as well as the spiritual energy present, we must delve into what is spiritually taking place.
The Maharal of Prague explains that since everything in the physical world is a manifestation of a spiritual root, when one studies the natural world and its seasons he can understand the spiritual energy of that time of year (Gevurot Hashem, 46). The fifteenth of Shevat marks the day on which the rain's potential growth begins to materialize through the trees producing fruit. The Ohr Gedalyahu explains that rain in this context does not only refer to physical water from above that leads to production and growth on land, but also alludes to spiritual Divine assistance that can aid in producing spiritual fruits, i.e. mitzvot (which are often referred to by Chazal as “fruits”; see for example Sotah 46a). The amount and nature of this Divine assistance is decided every Rosh Hashana, as it is on this day that
According to this symbolism the tree is also not only referring to physical trees but also to man; as the verse in the Torah says, "for man is like the tree of the field" (Devarim 20:19). The Shem M'Shmuel points out that just like a tree is the medium through which the ground can produce fruit, so too man is the medium through which physicality can be uplifted to produce fruit, mitzvot. The only difference between man and a tree lies in where the roots are implanted. Unlike the tree, man's roots are above, they are his intellect. All of his actions — his branches — all stem from his intellect, his roots. A physical tree, however, is rooted in the physical earth, and the rest sprout forth from that physical core. Indeed, as the Maharal explains, man is an upside-down tree (Chiddushei Aggadot, Sanhedrin 91b).
Based on the above we can understand the significance of the day of Tu B'Shevat. Just like the trees begin to bear fruit on this day from the rains of the new year, so too this is the time when we begin to see the results of the spiritual rains that we have received since Rosh Hashana. Because we have completed one-third of the new year, Tu B'Shevat is the opportune time to both harvest and assess the spiritual fruit of our labor. It is the happiness that accompanies this spiritual harvest that results in refraining from the tachanun prayer.