Petrified wood is wood in which the organic material has been replaced by crypto-crystalline quartz during the process of fossilization. Much of the delicate structure of the wood is preserved in the process because of the small size of the crystals.
Just like the organic material of the decaying wood is replaced by minerals, we too go through a process of metamorphosis in which our hearts are changed by the Lord. This process is known as purification and is a natural occurrence in mortality.
The Lord cautions us to soften our hearts, to remain pliable and teachable, so that the purification process can run its natural course, strengthening us spiritually for exaltation, "that Christ may dwell in [our] heart[s] by faith (Ephesians 3:17). We each must learn "to sanctify the Lord God in [our] heart[s]" as Peter taught.
The natural man (or the basic fiber (wood) of our being) is not strong, though at times it may appear to be. Unless we experience the mighty change in our hearts mentioned in Alma 5:14, we will never become what we could become. We will not be able to replace that which is weak within us with that which is strong.
We often think that by our own efforts we can do these things, but left to our own devices what we actually end up doing is hardening our hearts rather than being humble and allowing the process of purification to take place.