Machzor Mesoras HaRav with commentary adapted from the teachings of Rabbi Joseph B. Soloveitchik, pp. 102-103:
The Gemara in Horayos (12a) states that kings of Israel were anointed at a spring, as a portent that their reigns should be enduring in the same way that a spring continually brings forth water. Based on this concept, Abaye infers that omens in general can be significant and he therefore suggests that on Rosh Hashanah, one should eat specific foods whose designation imply good tidings for the coming year. The Rav explained that just as on the Seder night, there is a mitzvah to demonstrate that one has himself left Egypt, there is a similar imperative on Rosh Hashanah to demonstrate that Hashem is King over the entire world. Just as the environment in which a king is anointed should be symbolic of success and good fortune, on Rosh Hashanah we similarly engage in certain actions which are symbolic of a day on which we are judged by the King of the world. The mitzvah to show honor for the day (כבוד) on Shabbos and Yom Tov is fulfilled through actions such as bathing (prior to the onset of the holy day) and wearing clean garments. On Rosh Hashanah, this mitzvah includes a duty to symbolically demonstrate that the day is a day of judgment (Questions and Answers on Rosh Hashanah, September 25, 1978).