If you start an incremental search while the minibuffer is active, Emacs searches the contents of the minibuffer, as in any other buffer. Unlike searching an ordinary buffer, the search string is not shown in the echo area, because that is used to display the minibuffer.
If an incremental search in the minibuffer fails to find a match, it tries searching the minibuffer history. See Minibuffer History. Emacs pretends that the minibuffer and its history are a series of pages, with the earliest history element on the first page and the current minibuffer on the last page. A forward search, C-s, searches forward to later pages; a reverse search, C-r, searches backwards to earlier pages. Like in ordinary buffer search, a failing search can wrap around, going from the last page to the first page or vice versa.
When an incremental search in the minibuffer finds a match that is part of a history element, that history element is pulled into the minibuffer and displayed. If you exit the incremental search normally (e.g., by typing RET), it remains in the minibuffer afterwards. Canceling the search, with C-g, restores the contents of the minibuffer to what it was when you began the search.