When you sign up for a Twitter account, the default account settings allow anyone, whether or not they have a Twitter account, to view your profile, follow you, and see your tweets. If you want, you can make your Twitter account private so that only those Twitter users who are approved by you can follow you and see your tweets.
The feature of protected tweets is quite useful if you want to control who can see your tweets. This let's you create something like a closed group on Twitter and only the members of this group can see your updates. Since protected tweets cannot be retweeted, it further adds to your privacy.
Let's see how you can make your Twitter account private and protect your tweets
Sign in to your Twitter account and Go to the security settings page. To go to the security settings page, click on the gear icon at the top-right, then select Settings from the drop-down menu, and then click on Security and privacy on the left side. You can go directly to the security settings page at https://twitter.com/settings/security.
In the Privacy section, enable the Protect my Tweets checkbox as shown below.
Scroll down to the bottom of the page and click on the Save changes button to save the settings. Now, you can see the link to new follower requests on the left side on your Twitter homepage. You will have to approve your followers before your tweets are visible to them.