The word “mean” has many meanings. As a verb, it can indicate definition (Five means 5), significance (a smile means she’s happy), or intention (I didn’t mean to drop the cup).
In a mathematical context, “mean” is the same as “average”.
“Mean” can be used as an adjective for stinginess or miserliness.
When people say that someone is mean, it is usually because the person is intentionally cruel or hurtful.
Someone who is insensitive will hurt people by accident. Someone who is mean will hurt people deliberately.