When you block someone on Twitter this is what happens.

1. You and your Pic will not appear on the blocked person’s homepage
2. Your Tweets will not appear on their Timeline or badges
3. The person does not get notified that they have been blocked
4. They will not be able to follow you anymore or try to re-follow you or re-add you as a friend
5. They can still see your public profile but will be unable to receive your tweets on their public timeline or Phone
6. Immediately removed from their friends list
7. If they try to re-add you as a friend they will see this message