I'm definitely not versed enough to "explain" the logic behind "quantum algorithms" you'll just have to google it if you want to know more about it.

This "whole new layer of logic" that I was talking about allows computer scientists to construct algorithms that only a quantum computer would be able to run, because it follows rules that classical computers don't. For example, computational algorithms have been found (and devised) that would make prime factorization of large numbers MUCH more efficient for quantum computers than it currently is for classical ones. Prime factorization is one of the (if not the only) way of finding true primes which are used extensively in areas such as cryptography etc.

And you're right. For some tasks quantum computers would perform horribly when compared to classical computers, that's why you can't make the generalisation that quantum computing will "revolutionize" everything and make every computer in the world a thousand times faster.

Honestly, perhaps the only reason why scientists and engineers today are pursuing quantum computing is because of the fact that quantum algorithms for efficient prime factorization have been discovered and these algorithms (if run by an actual quantum computer) could defeat the most powerful encryption methods the world knows in heartbeats when compared to the millions of years it would take classical computers to break the encryption.