If you block someone on Twitter, they won’t be able to follow you or send you any messages. If your Tweets are public, they’ll still be able to view them, but they won’t show up on your followers list, and you won’t be on their following list.
How to block someone on Twitter:
If someone is sending you annoying messages or you simply don’t like someone then you can block them by clicking on their name to view their profile, then look for the button that says ‘follow’ or ‘following’, depending if you are currently following them. To the right of this button there is a person icon. Click on this and select ‘block @____’
Information gathered from Twitter FAQs.