Ok some what does non-binary mean?

She is a furry. Google it.

Non-binary is referring to the gender binary: man and woman. In Western society, typically we have assigned people to one of two genders, either man or woman depending on their genitalia. The two are typically considered mutually exclusive, if you are a man you can't also be a woman, hence the term binary (which is based off the binary code which features only 0 and 1 and is used for computers, which is where you might be running into the robot confusion). However, this gender binary and the gender roles that typically are associated with each gender (dresses for women, etc.) don't actually have any real basis. It is a social phenomenon we constructed, specifically in western society. In other cultures, it is normal and common for people to identify as a third gender or as neither gender. However, because it is so common in Western culture, to the point that people will punish others for not adhering to the gender binary, this person had to clarify that contrary to what is normally expected, they do not identify as either a man or a woman. This might initially be confusing and you might even think it's made up or annoying, but that's just your initial reaction to learning something new that doesn't immediately go with the way you normally think of things, but that's just a result of your own limited perspective. If you reflect on it for a moment you'll realize that it doesn't affect you and makes this person more comfortable, so who cares?

Side note, if they have told you they're non-binary they might no longer be comfortable with the pronouns she/her has those are usually used for women. Try and google the term non-binary if you want to read more about it, but try to look for LGBT-friendly sources and not just reactionary bullshit.