The biblical name for Rosh Hashanah is Yom Teruah.
Numbers 29:1 commands us to observe a Yom Teruah, on the first day of the seventh month. (Why the Jewish New Year is celebrated in the seventh month is another issue: suffice it to say that the rabbis list a total of four new years in the Jewish calendar.)
Teruah means a massive shout, either by a crowd or by a horn. For example, the walls of Jericho came tumbling down when the people (Joshua 1:20) “raised a mighty shout” (teruah gedolah).
This is a form of prayer and appears many times in Psalms — for example, “All you people clap your hands, raise a joyous shout (teruah) to God” (47:2).
As for meaning a shofar blast, during their travels in the desert, a teruah of the shofar let the Israelites know that it was time to move on.
Both of teruah’s meanings, supplicatory shouting and the sounding of the shofar, unite in Yom Teruah. It is a day of blowing the shofar and a day of prayer. The feeling of yearning exemplified in the shofar’s ululations are meant to inspire us to long to connect to God in a way that is beyond what words can measure.