This is a brand new feature on Twitter, and it's different than the "quote tweet" option on the mobile app; however retweeting with a comment is currently only available on your desktop computer.
Now, before we get into the details of how to retweet with a comment, let's talk about why. When you retweet another person's tweet, you're basically telling them that you like what they posted and you want to share it to your followers. With the "add a comment" feature, now you can add your own comment. This allows you to join the conversation and let your followers know why you think it's just a great tweet. What's even better, is that the tweet you're retweeting is added as an attachment, so you're free to use all 140 characters on your comment. When you quote a tweet, you end up cramming that tweet and your comment all into the 140 character limit...which is frustrating and not always possible.
Retweeting with a comment is fairly self-explanatory. When you're on your computer and you click the "retweet" icon, Twitter will automatically give you the option to add a comment. You don't have to do this. Clicking "retweet" without any comment will simply send the tweet to your followers as an auto retweet. If you'd like to add a comment, simply type it in the text box and click "retweet"!
Looking to learn more? Check this out.