The foundation for the simanim practice is laid by the Gemara (Keritot 6a) and the Gemara (Horayot 12a), where Abaye teaches that because a sign is a substantial matter, one should be accustomed to seeing or eating on Rosh Hashana foods such as gourd, fenugreek, leeks, beets, and dates — each of which grows quickly and serves as a positive omen for one's deeds in the coming year.
Building on that Talmudic precedent, the Tur (Orach Chayim 583) records the Ashkenazic custom of eating a sweet apple in honey at the start of the meal with the declaration "may a sweet year be renewed for us," and the Shulchan Arukh (Orach Chayim 583:1) codifies the full range of simanim — beans, leeks, beets, dates, pumpkin, and pomegranate — each paired with a verbal formula whose wording echoes the name of the food, while the Rema confirms the apple-and-honey custom as normative practice.
The Mishnah Berurah (583) clarifies that the apple is the primary food and its blessing covers the honey, and emphasizes that all these practices are done for a good omen — and that one must therefore be especially careful not to become angry during these days, so that the omen remain favorable.
At the deeper level, the Shem MiShmuel (Rosh Hashanah 7:9) explains that honey has the power to transform everything placed in it into honey, making it an active symbol of converting darkness into light and bitterness into sweetness — a fitting act for Rosh Hashana, which is the beginning and source before all differentiation, and therefore the moment when such transformation is most potent.
The Sefat Emet (Devarim, Rosh Hashana 1) adds that on Rosh Hashana one does not petition for worldly needs outright; rather, the simanim function as hints and allusions — pointers through which the spiritual vitality God renews for all creatures at the year's source is drawn down, provided each person is prepared to receive life solely for the service of God.