The Torah and Haftarah readings for Rosh Hashanah all connect with, and illustrate, one or another of the themes of the holiday. I use the plural advisedly here, because there have been a variety of readings from early on-long before the onset of modernity and the Reform movement.
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.