HAH - right up my ally. The one line answer is a Permineralization --- often the word "petrification" is used in normal discussion, but this carries the implication that ALL of the fossil has been mineralized. This is sometimes the case, but more often minerals entrap original organic matter of the organism. How does this happen? Well, minerals are borne in soil moisture (groundwater). These tend to precipitate out of the groundwater in open spaces. If, by example, you bury a tree, the cells lose their contents but the cell walls may remain for a long time before rotting. If these cells are invaded by a mineral-rich groundwater, then the mineral will precipitate out in the cavities created by the missing cell contents - trapping the organic material in the process.

Thus, the best "petrified" wood for scientific study is black in color, because it retains the original cell walls, trapped in a hard mineral matrix. Sometimes after a primary permineralization occurs, the cell walls will rot out, creating spaces - a secondary infiltration of minerals can then occur, indeed turning the whole fossil to "stone". Often these take on a variety of bright colors, but in this process the cellular detail is generally lost. These secondary replacements thus create colorful rock-shop items, but are often not of great scientific value. The most common mineral involved is silica (generally from volcanic ash), but calcite, pyrite and iron carbonate may also create permineralizations.

Actually, it is still called a fossil! When another mineral replaces original bone or shell material, we call this process replacement. Most fossils in rocks are changed from the original material in some way. In the process of replacement, molecules of original material are replaced one at a time. Two common types of replacement are calcification (replacement by calcite) and silicification (replacement by silica).

Permineralization is another process that can change original plant or animal remains. This is when voids are filled with new minerals. The most common example is petrified wood where silica has filled in individual plant cells.

The word 'permineralization' or 'petrification' leaps to mind, but a permineralization is where the mineral invades organic matter rather than replacing it (the original carbon in petrified wood is still there...).

Pyritization is where the tissues are being replaced or invaded by pyrite (pyritization is both rare and requires anaerobic environments). However, to get genuine replacement under normal circumstances, I think you would need your fossil to be mineral to start with - like the shell of a clam. That's just recrystallization.

There are a couple names that are applied to this process. One is called replacement where minerals replace the original organic material. One is called permineralization where minerals fill in empty spaces then the organic material disintegrates around it. The last type is called petrifaction (think petrified wood) and is a term that covers all types of fossils that have some or all minerals instead of organic material.