Originally, the concept of holography was developed in connection with visualization of very small systems like molecules. Dennis Gabor was awarded a nobel prize for his work in the development of holographic method. Building off the work of other physicists like Bragg who worked with visualizing molecules by X-Ray diffraction, his work still is relevant in different types of electron microscopy. Now however, the technique has been improved greatly due to the invention and use of lasers. In systems as small as molecules or atoms, its not too difficult to collect and analyze a diffraction pattern and then create a 3-D visualization of the molecule.
Technically speaking, holography refers to making a 3-D visualization of an object. So, those silver stickers on hats which appear to have a rainbow of colors when looked at from different angles are a type of holographic mapping. This "rainbow transmission" holography is simpler to make due to only needing a white light source and is often used in authentication.
However, the type of holography in science fiction is a tad more complicated. In science fiction, holograms are able to move, are viewable from almost all angles, and are of complex objects. Although advances are being made in this, for example, a holographic portrait of a person was recorded in 1971, making recordings of complex systems is still very difficult. The diffraction pattern that comes of a person is FAR more complicated, and difficult to work with than the smaller systems where holography was first developed. However, it seems quite likely, with time, newer technologies and more precise detectors that science fiction level holography will be possible.
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