Trying to understand this piece of code:
if [ -f /etc/bashrc ]; then
    . /etc/bashrc
fi
I'm not sure what the -f means exactly.
In short, the piece of code will source /etc/bashrc file if it exists, and the existence is verified by [ command to which -f is an operator/parameter.
if...then...else...fi statement in shell scripting evaluates exit status of commands - 0 on success. So it's proper to do something like this:
if ping -c 4 google.com; then
    echo "We have a connection!"
fi
The command, in your case, is [ which is also known as test command. So it'd be perfectly valid to do
if test -f /etc/bashrc; then
    . /etc/bashrc
fi
The -f flag verifies two things: the provided path exists and is a regular file. If /etc/bashrc is in fact a directory or missing, test should return non-zero exit status to signal failure
This command originally was a separate command, that is not part of shell's built-in commands. Nowadays, most Bourne-like shells have it as built-in, and that's what shell will use.
On a side note, the /etc/bashrc seems like  unnecessary extra file that your admin or original author of the code snippet is using. There exists /etc/bash.bashrc, which is intended as system-wide rc-file for bash, so one would expect that to be used.
See also:
The relevant man page to check for this is that of the shell itself, bash, because -f is functionality that the shell provides, it's a bash built-in.
On my system (CentOS 7), the fine man page covers it.  The grep may not give the same results on other distributions.  Nevertheless, if you run man bash and then search for '-f' it should give the results you require.
$ man bash | grep -A1 '\-f file$'
       -f file
              True if file exists and is a regular file.
$
    -f has nothing to do with if; it is an option for the [ command, which just happens to be called using an if statement here. Also, it just so happens that [ (along with if) is built in to bash.
                
                man [ in a linux terminal, you'll see that -f is an option of the [ operator. From there it's apparent what -f does.