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The description of man in its own man page contains the statement,

The default action is to search in all of the
available sections following a pre-defined order ("1 n l 8 3 0 2 5 4
9 6 7" by default, unless overridden by the SECTION directive in
/usr/local/etc/man_db.conf), and to show only the first page found,
even if page exists in several sections.

What exactly is meant by "1 n l 8 3 0 2 5 4 9 6 7"?

It's the "section" of the man-page - that number in parenthesis following the name, for example ls(1).

You could think of the man-pages as a set of actual manuals, divided into several volumes. For example, the 1st "volume" is section 1 which contains ordinary user commands - like ls(1), bash(1) and man(1). Section 8 contains commands for the system administrator - like commands for shutting down the system and install packages. (often commands that can't be used by non-root users.) Section 5 contains file-formats - like how /etc/passwd and /etc/sudo should be formatted. Section 3 contains library-functions for various languages (mostly for C) - like the C-function printf().

Note that some "commands" - like cd and fg - are really so-called built-ins in the shell, and don't have their own man-page. Instead they're documented in the man-pages for the particular shell - eg. in the man-page of bash(1). Shells may also provide alternatives to some commands as built-ins, and will usually use these instead of the external command. One example is how bash(1) got a built-in version of kill(1).

From the man-page of man-pages(7):

   1   Executable programs or shell commands

   2   System calls (functions provided by the kernel)

   3   Library calls (functions within program libraries)

   4   Special files (usually found in /dev)

   5   File formats and conventions eg /etc/passwd

   6   Games

   7   Miscellaneous (including macro packages and conventions), e.g.

       man(7), groff(7)

   8   System administration commands (usually only for root)

   9   Kernel routines [Non standard]

Sometimes letters or words are added to the number to denote the man-page belongs to a sub-system or package, for example, "x" for X GUI commands like startx(1x), or "tcl" for commands and functions belonging to the Tcl-language. Or even that they're "optional"/"additional" or "alternative" commands - for example, if you got two versions of tar, one from GNU and one from BSD.

To get a specific section, you can add the section-number to your man-command:

man passwd returns the passwd-command from section 1 (because section 1 is searched first, and the search then stops)

man 1 passwd returns the same (but now because we specified section 1)

man 5 passwd returns the file-format of /etc/passwd from section 5 (because we specified section 5 instead of 1)

To differentiate the two, you would refer to them as passwd(1) and passwd(5) (eg. if you wrote a textbook - or a man-page).

So the search-order makes sense - commands are more often sought than file-formats, not to mention programming libraries and system-calls.

Finally, you should note that different Unix-systems may use slightly different sectioning, for example, I've seen section 7 used for word-processing commands, and section 9 used for games, and I've seen section 9 used as a catch-all for various man-pages not fitting elsewhere.