Warning: Wikipedia contains spoilers
The plot concerns the search for a substance called ice-nine, an (imaginary) alternative structure for water which is solid at room temperature. The book follows the history of the creation and eventual "release" of ice-nine in a bombing, leading to the decimation of life on Earth as all water turns to ice-nine.
The title of the book derives from the string game "cat's cradle".
Note: Vonnegut's fictional ice-nine is not to be confused with the real substance Ice-IX (also pronounced "ice-nine"), which does not have the properties of Vonnegut's fictional ice-nine. See the article on ice for more details.