Note that this is just a warning, and Ruby should still run even with this Warning message.
It appears that /Users/Connor/.rvm/rubies/ree-1.8.7-2010.01/bin has permissions 766, which probably looks like this:
drwxrw-rw- 2 connor yourgroup 68 Apr 13 14:03 bin
This is not secure, because it means anyone with access to your system could install files under /Users/Connor/.rvm/rubies/ree-1.8.7-2010.01/bin, and you might execute those unknown files by accident.
Run this command from the commandline:
chmod go-rw /Users/Connor/.rvm/rubies/ree-1.8.7-2010.01/bin
This will disallow anyone but you from writing to and reading from that directory.