What does mean the mm e.g. 18 -200 mm camera or 55-200 mm?

That number is the focal length of the camera's lens ... which focuses light from the scene to form an image on the 'film' or CCD inside the camera. The longer the focal length of the lens, the larger (nearer) the objects appear to be in the picture. (One radian of angle as seen by the lens ===> One focal length on the film.) On the cameras described in the question, the focal length is given as a range ... "from 18 to 200 mm", and "from 55 to 200 mm". Each of these is a "zoom" lens, whose focal length can be changed over the range, enabling the user to cause objects in the picture to appear somewhat nearer or farther away.