The idea of quantum computing arose out of an attempt to make a better quantum mechanical simulator, which would allow for more efficient large molecule energy analysis, directly applicable to molecular biology.

The new computing model was later found to be generally useful and applicable to things like climate modeling too.

The simplistic intuition is that there are a lot of exact algorithms which are exponential, so we use clumsy polynomial approximations instead. A quantum computer makes many categories of exponential algorithms polynomial and therefore computable if a big and fast enough quantum computer can be built.