When you pay careful attention to doing a task exactly right, that's thoroughness. Your thoroughness in cleaning the kitchen means that no one would ever guess you spilled brownie batter all over the floor.
Thoroughness is seeing something through with meticulous care — the word's Old English root means "from end to end." The thoroughness of your research meant that you really knew what you were getting into when you adopted a puppy. A newspaper fact-checker's thoroughness means she'll get all the important details right, and printed articles won't include mistakes. And a detective's thoroughness might result in the return of your stolen laptop.