You will be in this mode only by accident (hopefully). This is the state Emacs is normally in (imagine!!). Now leave it as soon as possible by typing C-z. Then you will be in Vi state (sigh of relief) :-).
Emacs state is actually a Viperism to denote all the major and minor modes (see Emacs Preliminaries) other than Viper that Emacs can be in. Emacs can have several modes, such as C mode for editing C programs, LaTeX mode for editing LaTeX documents, Dired for directory editing, etc. These are major modes, each with a different set of key-bindings. Viper states are orthogonal to these Emacs major modes. The presence of these language sensitive and other modes is a major win over Vi. See Improvements over Vi, for more.
The bindings for these modes can be made available in the Viper Insert state as well as in Emacs state. Unless you specify your user level as 1 (a novice), all major mode key sequences that start with C-x and C-c are also available in Vi state. This is important because major modes designed for editing files, such as cc-mode or latex-mode, use key sequences that begin with C-x and C-c.
There is also a key that lets you temporarily escape to Vi command state from Emacs or Insert states: typing C-c \ will let you execute a single Vi command while staying in Viper's Emacs or Insert state. In Insert state, the same can also be achieved by typing C-z.States in Viper States in Viper Vi State