In a symmetric group, a transposition is a permutation which has the effect of swapping two elements while leaving everything else unchanged. More formally, it is a permutation of order $2$ which fixes all but two elements.

Example

In $S_5$, the permutation $\left(12\right)$ is a transposition: it swaps $1$ and $2$ while leaving all three of the elements $3,4,5$ unchanged. However, the permutation $\left(124\right)$ is not a transposition, because it has order $3$, not order $2$.