This article is from the Photographic Lenses FAQ, by David Jacobson with numerous contributions by others.
MTF is an abbreviation for Modulation Transfer Function. It is the normalized spatial frequency response of film or an optical system. The spatial frequency is usually measured in cycles per millimeter. For an ideal lens and ignoring diffraction, the MTF would be a constant 1 at all spatial frequencies. For all practical lenses lenses, the MTF starts out near 1 and falls off at increasing frequencies. MTFs vary with the aperture, the distance the image region is from the center, the direction of the pattern (along a radius or 90 degrees to that), the wavelength of the light, and the subject distance.
Even for an ideal lens, diffraction effects fundamentally force the MTF be be zero at spatial frequencies beyond 1/(lambda*N) cycles per mm, where lambda is the wavelength of the light. For lambda = 555nm, the peak of the eye's response, this is very close to 1800/N cycles per mm.
The MTF of a system is the product of the properly scaled MTFs of each of its components, as long as there are not two consecutive non-diffusing components. (Thus with proper scaling you can multiply camera lens MTF by film MTF by enlarger lens MTF by paper MTF, but usually not a telescope objective MTF by an eyepiece MTF. There are also some other obscure conditions under which MTFs can be multiplied.)
Note that although MTF is usually thought of as the spatial frequency response function and is plotted with spatial frequency as the abscissa, some manufacturers (e.g. Canon) publish plots of the MTF at specific spatial frequencies with distance from the center of the image as the abscissa.