Apodization (e.g., apodizing an image) is a method of improving an observation by physically manipulating the diffraction of the incoming electromagnetic radiation. The term is also used for a mathematical process to do an equivalent operation during signal processing.
Generally, the larger the aperture, the clearer the image, but the exact portions of the full image that are obscured depend upon both the aperture's size and its shape, and there are cases where a reduction in the aperture's size clears up some portions of the image, and the shape of this reduced aperture also affects precisely what's obscured. Given that a telescope's default aperture is generally as large as the physical telescope allows, one of the few possible methods of further clearing up specific image details is the clever use of masking to reduce the aperture's size, and (optionally) changing the shape.
An example is nullifying to some extent the distortion of an image due to Airy disks, by combining a telescope's image with that from a smaller aperture, e.g., reusing the same telescope with a mask. By this means, the extent of the distortion can be reduced, and two very close objects can be resolved, which the telescope's angular resolution suggested by the Rayleigh criterion would rule out, especially when one source is brighter than the other. Adjusting the shape of the aperture can also have useful effects.
The star-like shape of the starshade design, which is designed to limit diffraction of the star's light to the center of the shadow, is termed apodization.