It has a specific purpose, in my opinion. It generates some great Twitter analytics quickly (within 5-10 minutes for some of the reports) and saves them, if you log in.
If you analyze a Twitter user's followers, for example, you can show where their followers are located (up to 5000 of them). You can also see what the most common one-word and two-word strings are, to see if the followers are as targeted as they should be.
I often pull these reports up in the middle of meetings, to demonstrate to prospective clients how poorly their Twitter accounts are performing.
Unless you have a Moz accounts ($100/mo) you cannot do much with the date they provide other than look at it. Followerwonk does allow you to sort/follow/unfollow users, but only with that subscription.
One of the best features (and it's available in the free version) is the syncing with Buffer option once it analyzes which time zones your followers are in. Tweriod does this as well, but it costs $5 to get all the data on your followers' time zones (although Tweriod provides more data). So if you're running low-cost Twitter accounts, this is helpful.
1. The 5000 follower limit in an analysis is frustrating. It means you need a higher powered tool like SimplyMeasured, UberVU, or Brandwatch, to dig deep into your followers' topics and locations, or you'll only be looking at a small segment if you want to analyze a big Twitter account.
2. Since you need to subscribe to Moz to get the full value of Followerwonk, the tool doesn't really make sense. It's clear that SEOMoz just launched Followerwonk and let it be, because it doesn't fit within their SEO tool offering... Why do they only analyze Twitter, anyway?
Everyone has a need for social analytics on the go, and Followerwonk is a great solution. And when you're optimizing your Buffer scheduling for Twitter (which you should always be doing, since so few other tools provide scheduling queues like Buffer's), it's a cheap and easy solution.