Two-dimensional objects (e.g., the graph of a curve, letter of the alphabet) may have a line of symmetry, but cannot have a plane of symmetry because it would need to have 3 dimensions, and it is lying in a 2-dimensional plane already.
3-dimensional objects (e.g., a diamond, an ice cube) cannot have a line of symmetry because no line (which has only one dimension) can divide a solid into equal halves, but a (2-dimensional) plane can, so it can have a plane of symmetry which divides it into two halves of equal shape and size. It can also have an axis of symmetry, e.g., a planet has an axis of symmetry, a line through the north and south poles.