admin/environment/php extension/zip
From MoodleDocs
The native PHP zip extension is required to let Moodle 2 read or write ZIP compressed archives.
Installation on Linux Systems
If your distribution doesn't include this extension by default, then you need to compile PHP yourself and include --enable-zip.
This general PHP configuration will work well with Moodle 2.0:
./configure --with-apxs2=/usr/sbin/apxs --enable-mbstring --with-mysql=/usr --with-pear --enable-sockets --with-gd --with-jpeg-dir=/usr --with-ttf --with-freetype-dir=/usr --with-zlib-dir=/usr --with-iconv --with-curl --with-openssl --with-mysqli --enable-soap --with-xmlrpc --enable-zip
Installation on Windows Systems
Uncomment this line in your php.ini:
extension=php_zip.dll