The typical example is Shor's algorithm
https://en.wikipedia.org/wiki/Shor%27s_algorithm
It allows to efficiently find the prime factors of an integer - a problem without a known polynomial algorithm on a classical computer.
This would directly break RSA encryption, as it relies on factorisation being difficult.
https://en.wikipedia.org/wiki/RSA_cryptosystem
However, there are encryption algorithms that are considered safe even against a quantum computer.