Almost all of the modern world's computer security is based on some math problems that no matter how fast conventional computers get, will remain unsolvable in a lifetime.
In very generic terms, it boils down to the fact that when you multiply two large prime numbers, it is difficult to factor them (figure out which two large prime numbers that you used).
A quantum computer, in theory, can attack the factoring large prime number problem in ways that conventional computers can't. If they are able to factor large prime numbers sufficiently fast, the person or organization using that computer can also break encryption keys and blockchains. Basically anything that resembled computer privacy (or cryptocurrency for that matter) would be visible and accessible to that person or organization. It's a pretty immense jump in capabilities (in theory), and represents a capability that would be very powerful in today's world, potentially more powerful than a nuclear arsenal.
This stuff will be used to make new drugs and new materials that people can’t even dream of now.