When your Twitter account is set to private, only your followers can see your tweets. To make your account public, change the Protect My Tweets setting in the Security & Privacy section of your Twitter account's settings panel.
Click the Profile icon in the top corner of any Twitter page and select Settings on the drop-down menu to load your Settings panel.
Click the Security and Privacy tab on the left of the screen.
Scroll down to the Privacy section, if necessary, and remove the check mark from the Protect My Tweets check box.
Scroll down to the bottom of the page and click the Save Changes button. You may be prompted to enter your account password before Twitter will save your changes.
If you’re using the official Twitter app on your mobile device, unprotecting your tweets work a bit differently:
On an iOS device, touch the "Me" tab, tap the Gear icon and select "Settings" to open the Settings panel. Tap the name of the account you want to change and toggle the switch under the Protect My Tweets heading to the Off position.
On an Android device, touch the three-dot "Menu" icon in the top corner of the official Twitter app and select "Settings." Touch the name of the account you want to change and remove the check mark from the "Tweet Privacy" check box.
Once your account is public, your new tweets and all of your old tweets are viewable by the public.