An exacting person has high standards and expects nothing but perfection from themselves and others. They can be quite demanding.
When talking about someone being exacting, it's usually because they have very high expectations for how things should be done. Imagine a teacher who always checks your math problems twice to make sure you got them right, or a friend who's super picky about how their room is organized. That's an exacting person - they want everything just so and won't settle for anything less. This can sometimes make others feel like they're not good enough, but it's also because the person in question genuinely believes that better is always possible.
Making great demands; difficult to satisfy.
