Question

What does Rachel Carson mean when she suggests that man has acquired significant power of alter the nature of his world

Answer 1

She meant that the human race has acquired the ability to alter
the nature of the Earth.

Examples of a few neat things that we have the power to do:

-- Spread diseases to other continents from where they are.

-- Hunt and kill entire species of animals to extinction.

-- Eradicate the habitat of whole species so that they can't survive.

-- Poison the air and water over an area large enough so that
entire species become extinct.

-- Poison the air well enough so that species of vegetation ...
plants and trees ... are wiped out.

-- Extract so many members of a marine species from the ocean
that the entire population dies, along with other different species
that we're not even interested in but need the species that we
wiped out, in order for THEM to live.

-- Add enough stuff to Earth's atmosphere to change the climate
distribution on the planet, move the hot and cold places around,
move the wet and dry places around, and force the migration of
almost every living thing on Earth ... wiping many of them out.

It took us a while to learn how to do these things, but we are so smart
that we were able to stick to it until we succeeded.

By the way ... you really ought to go back and read this answer again, and
in the places where I wrote 'species', remember that human beings (us)
are one of the Earth's species.