Example problem: Find out which two prime numbers were multiplied together to produce the following semiprime:

25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952634432190114657544454178424020924616515723350778707749817125772467962926386356373289912154831438167899885040445364023527381951378636564391212010397122822120720357

A sufficiently large Quantum Computer that runs Shor's algorithm solves this problem in polynomial time, i.e. in hours to days.

Your classic, digital electronic super computer running the best classical algorithm (General Number Field Sieve or GNFS for short) would crunch this problem until the universe dies of heat death.

The semiprime factoring problem is a at the heart of public key encryption algorithm known as RSA. There's also another algorithm in public key cryptography called Diffie-Hellman, that relies on a problem called discrete logarithm. DH can also be solved with an algorithm closely related to Shor's algorithm.

Computers rely almost exclusively on these two problems e.g. to verify authenticity of files, software updates etc, and to establish encryption keys over insecure channels.

The modern society depends on computers for everything so understandably this is a big and important topic, and the reason NIST just recently completed a competition to find so called post-quantum algorithms that the society can rely on for the next thousand years.