On Rosh HaShana, God’s desire to rule over the world is renewed. On this day, one is required to accept God’s kingship upon himself.

Rosh HaShana contains within it everything that will occur over the course of the year:

All the months are called “the months of the year” (Exodus 12:2), whereas Tishrei is called, simply, “month” (Psalms 81:4). It is a general renewal of all worlds and their coming into being from nothingness, because Rosh HaShana takes place in it, and [Rosh HaShana] represents [in kabbalistic symbolism] the head and the brain of the year… just as a soul has [the aspect of] head and brain, from which is manifest the general life force, from which spreads the particular life force of each organ in accordance with its own nature and attributes, so too…on Rosh HaShana there is a manifestation of the general life force, and from it, the distinct spiritual force of each month is drawn.

The judgment on Rosh HaShana concerns accepting God’s kingship:

The principal time in which [God’s] will [to rule over the world] is manifest is on Rosh HaShana, when there is a renewal of the general life force for the coming year. The manifestation of the general life force of the previous year is understood to depart at the beginning of Rosh HaShana evening. Therefore, Rosh HaShana is the day of judgment, on which people are judged for their actions during the past year. For the possibility of a renewal of the general life force for this year [is in question because] there are a number of [angels making] accusations against humankind with regard to whether they deserve His heavenly will to be manifest in the revelation of His kingship. [These are] due to [occasions where] they cast off the yoke [of God’s kingship]. Some do not constantly accept the yoke of the kingdom of Heaven willingly and with love, but do so only occasionally, when they recall the King of kings, the Holy One, blessed be He. On the contrary, such a person is preoccupied with his own thoughts, each according to what is in his mind. In particular, there are those who are neither careful to abandon evil nor to do good, each person on his level. For the manifestation of the will of Heaven to reveal His kingship [and renew life in this world] is impossible when below, God forbid, there is casting off of the yoke of the kingdom of Heaven, when people do not willingly accept upon themselves the yoke of His kingdom. (Rabbi Shneur Zalman of Liadi, Likutei Torah, Rosh HaShana 53:4)

The Ba’al Shem Tov once instructed one of his students, Rabbi Zev Kitzes, to study the mystical intentions associated with the service of sounding the shofar, since he would be the one to sound the shofar for him [the Ba’al Shem Tov] on Rosh HaShana. Rabbi Zev studied the mystical intentions and wrote them on a special piece of paper and put the paper in his pocket so that he would be able to look at it during the sounding of the shofar. This did not please the Ba’al Shem Tov, and the paper was lost. When Rabbi Zev was about to sound the shofar, he began searching for the paper with the mystical intentions on it, and since he could not find it, he did not know which intentions to have. This greatly distressed Rabbi Zev and he wept bitterly with a broken heart while he was forced to sound the shofar without any intentions.

After the prayer service, the Ba’al Shem Tov said to him: In the king’s palace there are many rooms and halls, and there is a different, unique key for each door, but there is one instrument with which it is possible to open every lock, and that is the ax. The mystical intentions are the keys to the heavenly gates, and for each gate there is a different intention, but a broken heart can unlock each and every gate and hall.

After the shofar is sounded, a new, higher light descends; a light so heavenly that has never shone before. (Rabbi Shneur Zalman of Liadi, Tanya, Igeret HaKodesh 14)

Further reading: For the Ba’al Shem Tov statements on a broken heart as the key to every gate, see p. 308.