If you’ve blocked someone on Twitter they can still see your tweets.
They can always see them by logging out (unless your account is also private) but all of the third party apps I’ve tested will also let them see your tweets while still logged in. Official Twitter apps (Twitter for Android, Twitter for iPhone) don’t seem to and if they look at your profile they’d find they can’t.
In short, what people can see when you block them depends almost entirely on the app they use.
If you have access to more than one Twitter app and someone has blocked you then you can find out what you can see of their tweets by using the testing script below. If I’ve blocked you using the @FriendlyBlocker twitter account then replace username with that.
from:username – when using official Twitter apps (mobile or desktop Twitter) if you see nothing at all with this search then it’s likely that either they’ve blocked you or their account is private. Try using desktop Twitter while not logged in to see if you can see anything. If you’re using a third party app and you can see their tweets then you can’t tell from this alone whether they’ve blocked you (check on official Twitter, or try and favourite one of their tweets – note that if they haven’t blocked you this will send them a notification). If you can’t see their tweets on a third party app it’s more likely that their account is private (and they’ve blocked you, or you weren’t following them).
to:username – this will show you all tweets sent to a person, from which you can probably infer a fair bit of any conversation they’ve been having. If you click on a tweet that’s obviously a reply and you can’t see anything from them while using a third party app then their account is probably private.