Easier example. Say you have a 2d object, like a snowflake. Within 2d you can only rotate it clockwise or anticlockwise. If we put it in 3d, we can also rotate ut around the x, y or z axis and thus make a mirrored version.
Similar in 3d. Say you have a solved rubiks cube. Within the 3d space, you can never rotate it so only 2 sides change place (say yellow and white (which are opposite)). However, if we move to the 4th dimension, such a rotation is possible and we now have a mirrored rubiks cube.