Its possible that Adventure Time defies logical description, but we'll have a try. In the future, 1000 years after The Mushroom War, human boy Finn is raised alongside talking, shapeshifting dog Jake in the land of Ooo, which is a sort of post-apocalyptic earth where everyone has evolved into talking cupcakes and the like. Finn and Jake have adventures, often involving characters like Princess Bubblegum, who is Princess of the Candy Kingdom and made of, well, Bubblegum. Their main antagonist, the Ice King, is a flying, bearded Ice Wizard obsessed with capturing Princesses (of which there are dozens) but it later turns out he has a surprisingly adult, tragic backstory. And that's not even scratching the surface.
A typical episode involves Finn and Jake getting involved in some sort of strange, anything-can-happen quest, often resolved by what is best described as "dream logic" - there is a cause and effect at work but it's skewed. The world is colourful, and fast-paced, but loaded with sub-text and analogies and spoofs and in-jokes. Over the course of a few episodes, you start to feel the rhythm of it, and piece together a wider picture of the world and it's continuity that is more consistent than at first it appears.
Also after seeing a few episodes I'm not surprised that Adventure Time has picked up a substantial following. For a start its very fond of hinting at wider histories and relationships between its characters, it "ships" like crazy, and is full of insular nods and in-jokes to itself. In many ways it reminds me of Futurama, although that may be due to Jake sharing a voice with Bender. Its also got very strong visual design, and every con I've been to in the last couple of years (yes, I know thats not that many, shut up!) has had a couple of Finns wandering around it.
It is without question one of the wierder shows on TV at the moment. It is also fun, warm and engaging, and has ended up being a firm favorite with all four geeks in our house!