In the Hebrew calendar, the 15th of Shvat is known as "Tu biShvat" (Tu being the Hebrew letters Tet and Vav, which together add up to 15, hence the 15th of Shvat). In the Mishnah, our sages mention this date and call it the New Year of the Trees.
The significance of a new year for trees is important because it relates to the time when different offerings from the produce of the field (in Hebrew, Terumah and Maaser) had to be separated. Halakha—Jewish law—stipulates that offerings cannot be separated from the fruits of one year instead of those of the previous year, because these offerings sometimes varied. Therefore, it is important to know when the year changes, and in relation to trees, this change occurs on the 15th of Shvat. (This date is directly related to the cycle of the seasons and the time of year, in the Northern Hemisphere, when the fruits of the trees begin to grow.).
Today, as a way of commemorating Tu BiShvat, it is customary to eat fruit, particularly the fruits with which the Land of Israel is praised in the Torah: wheat, barley, figs, grapes, pomegranates, olives, and dates. It is understood that we should draw some lesson from all matters in the Torah, and this also applies to Jewish customs. Regarding the aforementioned custom, it is clear that people eat fruit on Tu BiShvat, but not wheat and barley. One simple reason would be that they are not edible as found in nature, but must be processed. Another reason is that they are not fruits of trees, but of the earth, and therefore have no direct connection to the New Year of the Trees.
The Rebbe explained another, deeper idea in a talk. Wheat and barley symbolize the basic foods that human beings need. Tree fruits symbolize additional and pleasurable foods, so to speak. The fact that on Tu BiShvat we eat tree fruits and not wheat and barley expresses the idea that we should serve God with all our qualities, not only the most basic but also the most profound, such as pleasure.
The soul contains specific qualities, some intellectual and others emotional. Each of these qualities is expressed in a particular part of the body. Furthermore, there are more general qualities that are found throughout the entire body and permeate everything, such as pleasure. When serving God, a person may fulfill a commandment with love for God, with fear of God, and even with enthusiasm and energy (chayut, in Hebrew), but do they enjoy it? The concept of utilizing the soul's quality of pleasure in serving God means, simply put, that the person enjoys serving God and does not do it merely out of love, fear, or obligation.
This is what the fruits we eat on Tu BiShvat symbolize, a way of expressing our desire to find pleasure in serving God.