Objectivity is a noun that means a lack of bias, judgment, or prejudice. Maintaining one's objectivity is the most important job of a judge.
The meaning of objectivity is easy to remember, when you see that the word "object" embedded within it. While it can be hard to show objectivity about people or pets, it's easy to be more "objective" about objects. I can show objectivity about a box of rocks; it's much harder to show it with my dog. The opposite of objectivity is "subjectivity," which is personal bias or opinion.