1. Tells you what app or platform someone's used to send a tweet
2. Lets you see the tweets of someone who's blocked you
I daresay other apps will let you do these too.
1. What app?
In the tweets below you can see that one says sent 'via Twitter Web Client' which means I sent it from my computer and the other 'via Echofon' which means I sent the tweet from my phone's app.
There probably aren't many times you'd need this information but I have used it in a vaguely 'forensic' sense to help someone strongly indicate that someone else sent a tweet themselves and that it wasn't automated. A big caveat is that the 'via Twitter Web Client' would also appear if I had used the Chrome browser app on my iPhone to send a tweet.
2. See tweets if blocked
I had been blocked by a homeopathy enthusiast for some time, without realising it, because their tweets showed up on the #homeopathy hashtag which I occasionally entertain myself with on desktop Twitter. If I click on their username on desktop it tells me I'm blocked but if I click on their name on Echofon it just shows me all their tweets, followers / following etc. Echofon doesn't appear to distinguish accounts blocking me from accounts not blocking me - I can't favourite or retweet a tweet, but otherwise if I was using only Echofon I'd probably not realise.
On any app or platform (possibly with the exception of Twitter for Android) you can simply search the person's username to see alll of their tweets (and replies. To see only their tweets use from:name). Or log out, of course.
Twitter's information about public / private tweets https://support.twitter.com/articles/14016#
Free ad-supported Echofon is also very annoying in that it regularly and frequently auto-opens the App Store on the iPhone in an attempt to get you to buy in-app purchases. It did it 7 times in 45s once but that's unusual, it goes through phases of not doing it for ages and then does it once every 20 seconds for a short while. On an iphone quickly double-tap the home button at the bottom to minimise all apps then swipe upwards on the trying-to-open-itself App store.