Edit link: https://github.com/dvyukov/go-fuzz
For example, a mutation may be changing a '==' to '!='. Your test suite is then run over the mutated source code and the mutant is said to then be 'killed' if at least one test fails. This is repeated many times, each with a different mutation to your source code. Your test suite is then given a mutation score based on the number of mutants killed divided by the total mutants.
Of course, there are some mutations that actually produce functionally identical code to the original. This means it isn't always possible for your test suite to kill every mutant.
Because many different mutations are made, with each one resulting in your test suite being run, mutation testing can become expensive. Having only read the abstract, this looks to be about a way for determining parts of source code not worth mutating, hence reducing the amount of times your test suite needs to be run.
Very short answer. Fuzzing changes run-time input and mutation is changing the code.