Rosh Hashanah Behavior
The Gemara (Keritot 6a, Horayot 12a) establishes that "Simana Milta", things we do on Rosh Hashanah act as a "omen" and have an impact upon the coming year. Many carefully partake certain foods on Rosh Hashanah as a good "Siman". So strict are some that if one does not enjoy any of these foods, it is sufficient to simply point to the food and recite the "Yehi Ratzon" prayer.
The concept of Simanim extends to behaviors as well. One should exercise extra care not to become angry on Rosh Hashanah, since one's conduct on Rosh Hashanah sets the tone and serves as a Siman for the rest of the year. The Talmud Yerushalmi famously remarks that if one naps on Rosh Hashanah, his "Mazal" (fortune) for that year likewise sleeps as well [The Arizal permitted sleeping after midday if a person feels tired, but one should make a point of remaining awake from daybreak on Rosh Hashanah, until at least midday].
Modern communities encourage the eating of these traditionally foods on Rosh Hashanah not as a "talisman" but rather as a statement of one's renewed effort to make the new year better by our actions and deeds. These rituals can symbolically express our wishes for the upcoming year.