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A common trend in applications of block ciphers over the past decades has been to employ block ciphers as one piece of a "Mode of operation" - possibly, a way to make a secure symmetric-key cryptosystem, but more generally, any cryptographic application. Most of the time, these modes of operation use a wide variety of techniques to achieve a subgoal necessary for their main goal: instantiation of "Essentially different" instances of the block cipher. The authors formalize a cryptographic primitive, the "Tweakable block cipher." Such a cipher has not only the usual inputs - message and cryptographic key - but also a third input, the "Tweak."
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