Completion Example
A concrete example may help here. If you type M-x au <TAB>, the <TAB> looks for alternatives (in this case, command names) that start with au. There are several, including auto-fill-mode and auto-save-mode--but they are all the same as far as auto-, so the au in the minibuffer changes to auto-.
If you type <TAB> again immediately, there are multiple possibilities for the very next character--it could be any of cfilrs--so no more characters are added; instead, <TAB> displays a list of all possible completions in another window.
If you go on to type f <TAB>, this <TAB> sees auto-f. The only command name starting this way is auto-fill-mode, so completion fills in the rest of that. You now have auto-fill-mode in the minibuffer after typing just au <TAB> f <TAB>. Note that <TAB> has this effect because in the minibuffer it is bound to the command minibuffer-complete when completion is available.
