Petrification is the process which replaces the organic matter from a dead organic matter to Inorganic minerals, but retains the structure of the object for future. Petrification occurs in absence or very little presence of moisture. Petrification of a living organism like plant is generally the process where the plant body is replaced by carbon or other minerals that are available abundantly in the surrounding, like silicification in sandy areas etc.
Animal dead body is generally replaced by calcium salts like calcium carbonate, which is the main composition of the bones. Hard parts are more well conserved than the flesh and fat, which melt away.