How should I understand “the fact” and “quality” in definition of a word

Question

I’m a foreign learner of English. I usually learn new words by looking at their dictionary definitions, and I often see “the fact of” and “quality of” in the definition of words. I get confused about what they mean.
In my native language, it just feels not right that these two words are used this way. As in this example, the definition of

variance: the fact or quality of being different, divergent, or inconsistent.

[Lexico]
So how can I understand these two words in a natural way? In addition, is it best to learn all new words by remembering their definitions?

fev · Answer

What is a fact?

something that is known or proved to be true.

So variance refers to the truth that something is different etc.
What is quality?

a distinctive attribute or characteristic possessed by someone or something.

So variance refers to things which are characterised by divergence, difference, inconsistency.
It is clear that "fact" and "quality" point to different aspects of a concept.
At different stages of learning, definitions may sound complicated and abstract, but they are there for a reason and are usually spot on. The best way to learn a new phrase or word is by seeing or hearing it used in natural real communications.

How should I understand “the fact” and “quality” in definition of a word

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