Our parasha lists several uses for the chatzotrot (trumpets) that Bnei Yisrael were commanded to make. They were used in the desert, where all Bnei Yisrael were encamped together, for gathering the people or the leaders and as a sign to travel (Bamidbar 10:2-7). The Torah goes on to list purposes that were used throughout generations when the people were in their own land – to turn to Hashem when war or other trouble appeared (ibid. 9) and to blast joyous sounds on "your happy day (yom simchatchem), your moadim (special days within the year), and your new months … on your burnt offerings and your shelamim offerings" (ibid. 10).
While most of the occasions are clear, the "happy day" is not. It is hard to say that it is referring to holidays because those are mentioned immediately thereafter. There are midrashim that attribute it to Yom Kippur, as we are happy to receive atonement, or Shabbat, which precedes the moadim whenever these days are discussed together (Parashat Emor and Parashat Pinchas). While these are extremely important days, we do not usually find the word simcha in their context.
The Netziv and Meshech Chochma say that it refers to the inaugurations of the Temples, whether it be the Mishkan in the desert or the dedications of the Batei Hamikdash. This is, of course, a very joyous occasion, and we do find that the gemara (Taanit 26b) says that the pasuk about Shlomo’s "day of his marriage and the day of the happiness of his heart" (Shir Hashirim 3:11) refers to the giving of the Torah and the building of the Beit Hamikdash, respectively.
The Ibn Ezra presents a very logical explanation. The day of joy is the day of victory in battle. Although the Netziv argues that we never find religious or political leaders in Tanach calling "days of happiness" after successful battle, the Ibn Ezra pointed out that we do find simcha in Tanach regarding Purim and the seven days of celebration that King Chizkiyahu called when the people of Yerushalayim were saved from Sancheriv’s troops (Divrei Hayamim II:30:23).
According to the Ibn Ezra, the juxtaposition works out beautifully. The pasuk just described blowing beseeching teruot with the trumpets before the war. The next pasuk goes on to mention the blowing of celebratory tekiot after the victory, which was aided by the trumpets ("… and you will be remembered before Hashem your Lord and you will be saved from your enemies" (Bamidbar 10:9).
The Chizkuni says that Hashem remembers, when Bnei Yisrael blow at the time of trouble, that they also blow when bringing sacrifices on holidays. According to the Ibn Ezra’s approach, this message rings especially clearly. Hashem realizes when we turn at the time of trouble that we will not forget, when we are successful, to thank Hashem for his Divine Providence that made the salvation possible (hopefully, this is the case). This, of course, is a lesson to remember in all generations, especially the last couple of generations, which have seen more successes in battle than we have seen in millennia.