complete is a bash builtin function. So there is not a binary on the system. It handles how commands will be completed when pressing tab.

Example: if you type:

user@host:~$ pidof <tab><tab>

...a list is appearing with all possible values for this command. In this case it means all running processes. See the output of the complete function:

user@host:~$ complete | grep pidof

complete -F _pgrep pidof

This means that the function _pgrep (-F) is executed when tabbing the command pidof. The definition of this function is in /etc/bash_completion.d/procps.

Another example: if you type:

user@host:~$ cd /usr/<tab><tab>

bin/     games/   include/ lib/     lib32/   local/   sbin/    share/   src/

...you see the list of folders you can cd to under /usr/. Which function is executed? greping the complete function (as above) tells us it's the funtction _cd in /etc/bash_completion.

Do it yourself: You have a program/script called /bin/myprog and you want that if you execute it as follows

user@host:~$ myprog /home/user/<tab><tab>

...it should only list folders, not files. So extend your bash completion with the following command:

user@host:~$ complete -F _cd myprog

That's it. You can also write own functions to complete custom things, for example complete only specific files or numbers or lists of static values...