Why are older parts of the ocean floor no older than about 200 million years?

The older parts of the ocean floor are no older than about 200 million years old is because of subduction. Subduction is "the sideways movement of the edge of a plate of the earths crust into the mantle beneath another plate."

This basically means that the ocean floor is renewed every 200 million years.

They are older because they were there before the new pats of the floor and only the new parts of the floor get washed away and the old parts stay.