"Normal" can refer to several things in Diablo 3 and Reaper of Souls.
Normal is the name of the lowest difficulty setting in Diablo 3 version 2 and Reaper of Souls. This is the default difficulty setting and offers no bonuses to item drop rate, exp or gold, etc.
Normal also refers to item quality. The plain, non-magical white items are often referred to as "Normal."
Normal may also refer to the basic form of active skills, as opposed to the rune effect forms that players use 99% of the time.