admin/environment/php extension/zip
From MoodleDocs
The native PHP zip extension is required to let Moodle 2 read or write ZIP compressed archives.
Native installations of php will need php zip library enabling by adding the line
extension=zip.so
to php.ini
However if your php was not compiled with the extension then...
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
Note: The Zip extension is built-in since PHP 5.3.x on Windows (from windows.php.net). The above php.ini line and the corresponding dll file is not require if using PHP 5.3.x or newer.