Mineral replacement fossils are fossils that preserve the
structure of the original organically produced matter without
actually preserving any of the original material.
The agatized shells mentioned above are a good example. An even
better example is petrified wood, which has absolutely no wood at
all in it - it has been 100% replaced with silica - but which
preserves structures sometimes right down to the cellular
level.
Typically these types of fossils involve silica, since silica is
often deposited as a colloid and ends up forming micro-fine
crystals that can preserve structures very well. Occasionally you
see other replacements such as pyrite replacing what were
originally shells.