Since Rosh Hashana is the Day of Judgment, each person should feel anxiety and awe. He should guard against levity and anything that distracts him from the awe of judgment.
So great is awe of judgment among Israel on Rosh Hashana that despite it's being a festival, they do not recite the Hallel song of praise recited on the New Moon or festivals. For Hallel is said only with a joy-filled heart, whereas during the days of judgment there should be more fear and trembling in Jewish hearts than rejoicing.
Thus our sages taught, "Said the angels before G-d, Lord of the Universe, why does Israel fail to utter song before you during Rosh Hashana and Yom Kippur? He replied, When the King sits on the throne of judgment and the books of life and death are before him, can Israel utter song?" (Rosh Hashana 32).
Nevertheless, a person should not be saddened by fear of judgment. One should have a haircut, wash, and wear special clothes in honor of the festival. A husband should also give his wife a gift in honor of the day, and buy treats for the children. This demonstrates our faith that G-d will show us favor.
So we find that when Ezra the Scribe read the Torah before the assembly gathered on Rosh Hashana, and all the people wept on hearing the admonitions of the Torah, Ezra and Nehemiah said to them, "Do not mourn and do not weep. Go eat delicacies and drink sweet drinks and send gifts to whoever has no food, for the day is sacred to our Lord..." (Nehemiah 6:10).
Similarly, our sages taught: "Usually, a person who has a judgment pending against him dresses in black and neglects his appearance in worry of the outcome. Israel however is different. They dress in white, they eat, drink and rejoice in the knowledge that G-d will perform miracles in their behalf [and forgive them]" (Yerushalmi, Rosh Hashana, ch. 1).