Sudoku puzzles are 9x9 grids of numbers, subdivided into 3x3 blocks. When you begin a puzzle, some of the numbers are already filled in, and you have to fill in the blank squares using logic. You must fill the grid so that all the numbers 1-9 appear in each row, column and 3x3 box. However, no row, column or 3x3 box may have two of the same number.
Sudoku puzzles first appeared in New York in the late 1970's under the title "Number Place". They were introduced to Japan in 1984 where they were renamed to Sudoku (pronounced sue-do-koo; su = number, doku = single), so Sudoku translates as "single number".
There are also many fascinating varients of Sudoku: Killer-Sudoku, which combines elements of Kakuro, Sudoku-X, where the diagonals must also be considered, and Mini-Sudoku, which use 6x6 blocks and numbers 1-6.