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The buffer `*scratch*' which is selected when Emacs starts up is provided for evaluating Lisp expressions interactively inside Emacs.
The simplest way to use the `*scratch*' buffer is to insert Lisp expressions and type C-j after each expression. This command reads the Lisp expression before point, evaluates it, and inserts the value in printed representation before point. The result is a complete typescript of the expressions you have evaluated and their values.
The `*scratch*' buffer's major mode is Lisp Interaction mode, which is the same as Emacs-Lisp mode except for the binding of C-j.
The rationale for this feature is that Emacs must have a buffer when it starts up, but that buffer is not useful for editing files since a new buffer is made for every file that you visit. The Lisp interpreter typescript is the most useful thing I can think of for the initial buffer to do. Type M-x lisp-interaction-mode to put the current buffer in Lisp Interaction mode.
An alternative way of evaluating Emacs Lisp expressions interactively is to use Inferior Emacs-Lisp mode, which provides an interface rather like Shell mode (see section AC.15.3 Shell Mode) for evaluating Emacs Lisp expressions. Type M-x ielm to create an `*ielm*' buffer which uses this mode.