Normally, I would put some clever hook about current media, pop culture, and/or politics to tell you why genders that aren't in the binary of Men/Women need to be recognized: but I can't because that's how much we are not acknowledging people like this to begin with. In popular culture we are quick to associate aliens (Doctor Who) with nonbinary genders because they are not even from this planet and we associate machines (Adventure Time) with potential nonbinary identities as well—yet we fail to consider actual human beings as not fully fitting into the concept of womanhood or manhood.
To begin, we need to clarify the most crucial point of this article: sex and gender are not the same thing. Biological sex is based around chromosomes, genitalia, and other bodily features such as body hair and breast structure. It is also important to note that someone can be neither male or female in assigned sex and be a combination of both or something else entirely due to chromosomes, genitalia, other bodily features, and even self-identity. This is called being intersex. Gender, as one of my friends describes it is the "heart part, not the private part," and is more about personal identity instead.
Given that sex is different than gender, which is hard enough for many people to grasp due to the relationship we've forged between the sex binary and the gender binary (both social constructs), it almost seems like there can be an infinite number of gender identities: and there are. Nonbinary itself is an identity of a gender that simply is, but is not in the gender binary. This term can include people who are intergender, identifying in between man and woman, genderfluid, an identity that fluctuates depending on mood or time from man, to woman, to any other identity, pangender, identifying with both binary genders and more (similar to bigender which sticks to the binary genders), and many more that can be found here, here, and many other websites about nonbinary gender identities. Most importantly, there are people that don't feel gender at all and feel more like themselves or as a human being; these people identify as agender, literally 'without gender'.
To people who have grown up on the social binary of male/female and man/woman, this may seem like a tidal wave of information or even that it's made up. Nonbinary gender identities as well as the identity of no gender at all are socially constructed in the same way that the identities of being a man/woman are created. The same way we respect the identities of being a man or woman, we should respect nonbinary identities because as Adrian Ballou says, "Gender…is something that is usually a deeper part of someone’s identity than a profession or sport – so we shouldn’t guess at it," or disrespect it. So, if we don't really know about this but don't want to seem disrepectful: what do we do?
Ask questions! While anyone can look up more information, some of the best information is unique by each person that identifies like this. Asking people who identify outside of the gender binary about how they identify and importantly, what pronouns they prefer, are crucial to respecting these persons. Pronouns, while they just seem like simple groups of words, hold the entire identity of a person. Nonbinary persons may use they/them pronouns (which can be used for singular a person), ze/zim pronouns, or even binary he/him or she/her pronouns. The biggest way to learn and be more accepting? Simply ask people how they identify and respect and validate that.