“…by which the world that then existed perished, being flooded with water.”
The word “which” is neuter plural and refers to two sources of floodwaters. Water came from the skies and from below ground (Ge 7:11; 8:2).
world that then existed perished, being flooded with water
The “world” here is the world of people. The Flood destroyed all inhabitants of the world except those on the ark. The whole state of things then existing perished.
We get our English word “catastrophe” from the Greek word for “flooded” [katakluzw]. It is not all that clear whether this is the flood of creation or the flood of Noah’s day. Whether Peter refers to the judgment of Noah’s day or pre-Adam judgment is conjecture. The important thing is that we realize that there was a catastrophe in the past.
The stability of the world depends entirely on God’s will.
God has sovereignly passed judgment on the world. He ultimately is in control of the universe. Our universe is not random, but God carefully and providentially manages the universe. He, at times, chooses to intervene in the universe.