You will be in this mode only by accident (hopefully). This is the mode Emacs is normally in (imagine!!). Now leave it as soon as possible by typing C-z. The you will be in Vi mode (sigh of relief) :-).
Emacs mode is actually a VIP'ism to denote all the major and minor modes (see section Emacs Preliminaries.) other than VIP that Emacs can be in. Emacs can have several modes, such as C mode for C editing, Dired for directory editing etc. These are major modes, each with a different set of key-bindings. VIP modes are orthogonal to these Emacs major modes. The presence of these language sensitive and other modes is a major win over VI. See section Improvements over VI for more.
The bindings for these modes can be made available in the VIP Insert mode as well as in Emacs mode. It is even possible to bind some keys in the manner of VI, and keep the rest according to the major mode. This means that you can use specialized behavior in Insert mode, and then jump back to Vi mode for any movement, deletion etc.
See section Customization, to find out how to do this.