Your web server is ran by a special user, probably "www-data". This user has to have permissions over the folders accessed by the internet in order to display them.

You can set permissions like this:
sudo chown -R username:group /path/to/folder

So your command might look something like this:
sudo chown -R www-data:www-data /var/www

After thats done restart your web server with:
sudo service apache2 restart