Definition:Latin Square

Definition
Let $n \in \Z_{>0}$ be some given (strictly) positive integer $n$.

A Latin square of order $n$ is a square array of size $n \times n$ for some containing $n$ different symbols, such that every row and column contains exactly one of each symbol.

That is, each row and column is a permutation of the same $n$ symbols.

Also see

 * Existence of Latin Squares: Latin squares exist for all $n$.