That was a new one to me too, but a bit of digging reveals that a tumbleblog (aka a "tumblelog") is a weblog written with a "stream of consciousness" approach, kind of like the traditional journal/diary that begat the entire blogging phenomenon.
Leo Babauta, over at the North x West blog, offers up this missive: 13 reasons why bloggers should use a tumblelog for links. In it, he explains:
"Let’s start by talking a little about tumblelogs. If you’re not familiar with them, they’re about the simplest blogs there are — basically a collection of links, quotes, photos, videos, dialogue, snippets of text, or anything else you might run into while surfing the net.
"A tumblelog can contain regular blog posts, but for the most part it’s links and other media you stumble across that you want to share with others. And it’s easy: you can use a service like Tumblr and get a free tumblelog running in minutes. Using their bookmarklet, you can link to a post or photo or video within seconds. No hassle, no wasted time."
Got it? I'd refer to this as a "linkblog", personally, but the idea is that you just spit out material in the tumbleblog, be it four words (like "too tired to blog") or a few paragraphs. The items don't have to be connected in any logical way, and, just as with any other kind of blogging effort, there are no rules about what is or isn't acceptable.
Having explained that, I have to say that most linkblogs and, presumably, tumbleblogs/tumblelogs I have encountered are useless to me, because they are focused more on resource location than on explaining why those particular resources are of value. If it's just a flow of consciousness, that's different, I suppose, but still, I am more interested in why than in what.
Meanwhile, you can learn more about tumblelogs by simply searching for that word (or tumbleblog, it appears that they're interchangeable) at Google Blogsearch or similar. No six-shooter required.
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I think my tumblelog (http://stumblng.tumblr.com) is a good example of the tumblelog type. I use software called tumblr. It's very easy to use, free and the tumblr people host your tumblelog. If you look at my tumblelog and have any questions about creating a tumblelog with tumblr, I'd be happy to hear from you at the email address shown on my tumblelog.