If you surf through pure http (without SSL) pages you should have no problem. But to surf through https (using SSL) websites, as Arminius said in a comment, you must to install Burp's certificate. Burp needs to perform a man in the middle to serve ssl pages to you using it's certificate.
Open your browser and open
http://127.0.0.1:8080 to access to burp's page. Download Burp's certificate clicking on
CA Certificate, is on the top right side of the screen. Once downloaded, install it on your browser. the installation steps may vary depending of your browser. Then you'll have no problems surfing ssl sites and you'll see https requests on your Burp's proxy HTTP history.