An omer is a measure of grain, in this case, barley. In the days of Temple worship, we were to bring the first sheaf of barley to the Temple, followed by other items, as a sacrifice (Leviticus 9–14).
There are many elements which make the High Holy Days a unique experience. Often, congregations swell to double or triple their usual size, the musical settings of even common liturgy are different, and some might alter their dress by wearing either traditionally all-white garments or more formal wear than they would sport on Shabbat. Some congregations even have unique garments to dress their Torah scrolls in white.