After you've finished typing, you can tap the '+' icon on the center toolbar and save it for later, or you can tap the 'Share' icon on the right side and export it to many different places, including Evernote, Tweetbot, SMS, Facebook, Reminders, Dropbox, Omnifocus, Sparrow, Agenda Calendar, and a lot more.
Drafts supports Markdown as well, if you're into that sort of thing. I've personally been using it as a tool for practicing Markdown on the go, since it includes options to preview the HTML output of your Markdown or send it elsewhere for use.
If you would like to go back and see all of your previous drafts, just tap the 'paper' icon on the tool bar and the keyboard will slide down, revealing the drafts list underneath. There's no organizational structure that I'm aware of (like folders or tags), but if you need to find any specific thing you can just use the search feature (obviously, it's the magnifying glass icon on the toolbar).
Drafts has become extremely useful for me, because I often have an idea spring to mind that I forget by the time I can get it into text form. I could just open Evernote and create a new note there, but Drafts feels so much more direct and I don't feel like I'm going to forget anything by the time it opens because it only takes a second or two.
With Evernote, I have to wait for the notes list to finish syncing, then tap the 'New Note' button, then tap in the body area to start typing. Those extra seconds really do matter, especially when you're doing those same things every single time you open the app. Plus, with Evernote, I'm tempted to properly tag and title each note when I'm done, but with Drafts I don't feel that compulsion. In this case, simple really is better.
There are plenty of other features in Drafts that I haven't even talked about here. For such a simple app, it's pretty powerful, and I highly recommend it. The iPhone version is $2 and the iPad version is $3.