It implies a meticulous and often demanding approach, showing a strong desire for perfection and a dislike of anything messy, careless, or imperfect.
Here are some examples:
* "She fastidiously cleaned her apartment, making sure every surface was spotless."
* "The chef prepared the meal fastidiously, using only the freshest ingredients."
* "He dressed fastidiously for the occasion, making sure every detail of his outfit was perfect."