Curl is a library that lets your make HTTP requests in PHP.
Most hosting providers have cURL installed already but if you have to install it on your self managed server with Apache and PHP5 installed, then follow this step by step process.
1. Install packages
apt-get install curl libcurl3 libcurl3-dev php5-curl php5-mcrypt
2. Open php.ini and add extension (my php.ini file is located at /etc/php5/apache2/php.ini)
3. Restart Apache