In this week's Parsha, Hashem instructs Moshe to make himself two חצוצרות כסף, trumpets of silver (במדבר י;ב). There are four seemingly distinct purposes enumerated for these trumpets (שם פסוקים ג-י). First, the sounding of these חצוצרות is to serve as a signal to the Jews that they should assemble at the Mishkan. They would also be sounded when it was time for the encampment of the Jews to prepare to travel. Third, during times of war and imminent danger, the חצוצרות would be used to "remind" Hashem to come to the aid of the Jews. Finally, the sounding of the חצוצרות would accompany the offering of Korbanos on special occasions like Yom Tov, serving as a זכרון, a commemoration before Hashem; it is unclear from the Pesukim exactly what is to be commemorated.
These four purposes can be divided into two basic categories: the trumpets were either to be Hashem's line of communication with the Jews, or their line of communication with Him. They could be used by Hashem to gather the people at the Mishkan, the earthly manifestation of His presence, or to instruct them to follow Him through the desert. Alternatively, they could be used by the people to beseech Hashem for assistance, or to recognize Him in their time of joy.
Based on the dual role of these instruments, we can clearly understand why they were to be sounded specifically by the Kohanim, whose role had a similar duality, as documented by the Gemara in Yoma (דף י"ט: ובתוספות שם בד"ה מי). On the one hand, they were messengers of the people to Hashem, bringing the Korbanos of the entire nation and thus allowing them to make requests of Hashem and give Him thanks. However, they also had a second role. They were to serve as messengers of Hashem encouraging the people to seek closeness with Him, especially through the medium of Korbanos. Just like the, חצוצרות the Kohanim serve as a link between the Jews and Hashem, through which both can communicate with each other. Throughout times of danger and celebration, the Jews are blessed with the ability to communicate with Hashem, and to be communicated with by Him.