The definition of a geometrical plane is "a surface defined by a minimum of three points". By definition, a plane is imaginary. The [median plane] is "a vertical plane that divides the human body standing in the anatomical position in two halves, left and right, that are equal in size" (although not in content).
The term "midline" is a bit of a misnomer, as this is a plane and not a line, although if you look at the median plane from the anterior or posterior aspect of an individual in the anatomical position, you would have a line, ergo, midline!
To visualize the above statement, click on this "anatomical position" link and hover your mouse over the image. The midline will appear.
Another term that can be used synonymously with [midline] or [median plane] is that of "midsagittal plane". Any plane that is parallel to the midsagittal plane (therefore not on the median plane) can be called either "sagittal" or "parasagittal".
Since planes are imaginary, the only way to make them real is to cut, section, or image following a plane, this is called a "plane of section"