Question

What does it mean and how can I fix it?

zsh compinit: insecure directories, run compaudit for list.
Ignore insecure directories and continue [y] or abort compinit [n]?

Running the compaudit returns the follows:

There are insecure directories:
/usr/local/share/zsh/site-functions

Answer 1

Note: This answer is from 2012.

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This fixed it for me:

$ sudo chmod -R 755 /usr/local/share/zsh/site-functions

Credit: a post on zsh mailing list

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EDIT: As pointed out by @biocyberman in the comments. You may need to update the owner of site-functions as well:

$ sudo chown -R root:root /usr/local/share/zsh/site-functions

On my machine (OSX 10.9), I do not need to do this but YMMV.

EDIT2: On OSX 10.11, only this worked:

$ sudo chmod -R 755 /usr/local/share/zsh
$ sudo chown -R root:staff /usr/local/share/zsh

Also user:staff is the correct default permission on OSX, where user is actually your username (i.e. whoami, or $USER). In other words:

$ sudo chown -R ${USER}:staff /usr/local/share/zsh