In crystallography, a Wyckoff position is any point in a set of points whose site symmetry groups are all conjugate subgroups of one another.
For any point in a unit cell, one can apply a symmetry operation to the point. In some cases it will move to new coordinates, while in others it will remain unaffected. For example, reflecting across a mirror plane will switch all points left and right of the plane, but points on the plane will not move.
We can test every symmetry operation in the crystal’s point group and keep track of whether the specified point is invariant under the operation or not. The finite list of symmetry operations which leave the given point invariant taken together make up another group, known as the site symmetry group of that point. By definition, all points with the same site symmetry goup, or a conjugate site symmetry group, are assigned the same Wyckoff position.