Keccak's structure is simple and markedly different from that of MD4, MD5, SHA1, and the SHA-2 family, all of which share a common design pattern called Merkle-Damgard (MD). MD-style hashes chunk their inputs into blocks and tag the last block with a length; they then run in a manner similar to a block cipher, where each block is combined with the previous block after the hash function core is applied. The resulting output of these MD-style hashes is literally the internal state of the hash at the last block; you can take most SHA-2 hashes, for instance, and "feed them back" to the SHA function with more data to generate a continued hash. This gives rise to a common crypto protocol flaw called a "length extension attack".
Unlike MD, Keccak uses a design called a "sponge function". It's called a "Sponge" because it splits hash into two distinct stages: one in which the hash function "absorbs" data, applying the hash core function to permute an internal state, and another in which the hash is "squeezed" to produce output (which further permutes the state). Somewhat like a cryptographic PRNG, the security of the hash function is delegated to the confidentiality of the internal state, which isn't disclosed by producing the hash.
Furthermore, Keccak's Sponge design derives security by only allowing inputs to directly influence a subset of the internal state bits. Like MD hashes, the inputs are chunked into blocks and fed to the hash algorithm. But each block fed to the hash affects only that block's worth of internal state bits; the remainder of the hash's state (called the "capacity bits") are mixed in with the "outer" bits during the application of the hash core. Here's a picture that may tell the story better:
http://tinyurl.com/cryptosponge
Notice how the "M" bits of the input hit only the "r" bits of "outer" state in the hash, while the "c" bits of "capacity" are used only during the "f" function.