Rosh Hashanah is Hebrew for chief of the year. It is the date elected for celebrating New Year according to the Hebrew calendar. It starts at sundown on 29th Elul & lasts for two days (1st and 2nd of Tishrei) except among Kairaites Jews, who only supervise the first day. Rosh Hashanah is the first of the Hebrew elevated holidays, Yamim Noraim /Days of Awe, the most solemn days in the Jewish year.
The month of Elul which precedes it is invented to be used by Jews for self-examination, & the Shofar (ram's horn) is blown every day to remind them of the coming judgement (except on Shabbat in orthodox communities). Unique prayers called selichot are recited in the synagogues every night Among midnight and dawn from the first or second Saturday before Rosh Hashanah up to the start of Rosh Hashanah, & on Rosh Hashanah itself religious poems called piyuttim are recited.
The ten days from Rosh Hashanah leading up to the Day of Atonement (Yom Kippur) are called the Ten Days of Repentence or Asseret Yemei Teshuva. Food at Rosh Hashanah often includes apples & honey to signify a sweet New Year. Depending on location such foods as dates, leek, tongue, spinach and melons are also commonly eaten, along through pomegranates and challah bread.