Twitter is testing a new feature that allows you to embed tweets within your tweets, provided you're using the official Twitter client for iOS.
To embed a tweet, you have to copy the link to the tweet and paste it in the text box of the app. The feature gives you the ability to add your own opinion about the tweet you're embedding, which isn't the case with the retweet option.
The embedded tweets (for now) aren't visible in the web interface and seem to be limited to the mobile app. To view the embed boxes, you have to click on the individual tweet, as the timeline still shows the embedded tweets as a URL.
Currently, it looks like Twitter is testing the feature out with select users, and may integrate it in a future update. To use the embed feature, all you have to do is use the latest version of Twitter's app, which you can download from the App Store link below.
Are you able to embed tweets via the mobile app? Is this a feature you would be interested in seeing in the web interface? Share your thoughts in the comments.