Folks, don’t click that.
There’s no way for any site to tell you what this is promising, just like no one can tell you who reads your Twitter page. It can’t be done (yes, yes Google Analytics, which isn’t nearly the same).
If you already clicked that, go to https://www.tumblr.com/settings/applications and click “Revoke Access” to at application you don’t recognize.
Oh, and you might want to delete that post that this app posted on your behalf, trying to get more people to fall for it.
Signal boost: what TJ said. If you want to know who’s looking at your tumblr (kinda sorta, at least by IP), install a tracker like statcounter or sitemeter. If you need help, ask me. Unlike this thing, I promise never to ask for your password.
If I were you, I’d revoke access from that thing. Who knows what it will decide to post on your behalf in the future.