magnification
Look through a magnifying glass and the print looks twice as tall; look through the wrong end of binoculars and the world shrinks. Both are described by magnification, the number that says how much bigger or smaller an image is than the actual object, and whether it is turned the right way up or flipped over. It answers the question: compared with the real thing, how tall is the image, and is it upright or inverted?
For a lens or mirror the (linear or lateral) magnification is m = h_i / h_o = -d_i / d_o, where h_i and h_o are the image and object heights and d_i, d_o are the image and object distances. The size of m tells you the scale: |m| greater than 1 means enlarged, less than 1 means reduced, equal to 1 means same size. The sign tells you the orientation: a positive m means an upright image, a negative m means an inverted (upside-down) one. So m = -2 means twice as tall and flipped upside down, while m = +0.5 means half-size and the right way up.
Magnification is what you are really buying in a telescope, microscope, or camera zoom, though for instruments made of several lenses the total magnification is the product of the magnifications of each stage. An honest caveat: a bigger image is not automatically a clearer or more detailed one. Magnify too far and you just get a large blur, the real limit on fine detail is set by diffraction and the quality of the optics, not by how many times you can enlarge the picture, this is the difference between useful magnification and empty magnification.
A slide projector's lens gives d_o = 5 cm and d_i = 300 cm, so m = -d_i/d_o = -60. The image on the screen is 60 times taller than the slide and inverted, which is why slides are loaded upside down.
m = -d_i/d_o: magnitude gives the scale, sign gives upright (plus) or inverted (minus).
A negative magnification is not a mistake, it simply means the image is inverted. And magnifying beyond what the optics can resolve gives empty magnification, a bigger but no clearer picture.