Since the incidents happened in March, twitter is taking all the security measurement it can. Twitter have enabled secure access to the entire portal (means you can access it as https://twitter.com against currently you are accessing it as http://twitter.com).
Right now, the secure site can be accessed manually by typing https:// as the protocol (instead of http://). But in a news company have enabled automatic redirection to https:// for a group of users already. In such case when you open a website in normal way, it will be redirected to its secure version (from http:// to https://) automatically. The company is planning to enable the stuff for entire portal (and hence for all the users/all the pages) in near future, once the testing goes fine.