At its most basic level intersex is any aspect of bimodal sex development that is different from expected perisex development. (Perisex refers to people who are not intersex)
CW: I'm going to use a lot of clinical language so that hopefully perisex people and people who are wondering if they themselves might be intersex will be better able to follow.
What do we mean by "sex"?
Sex is made up of a range of different factors. Factors like chromosomes, sex hormones, your bodies response or lack of response to certain hormones, genes and epigenetics. All of these factors come together to make your sex.
What makes somebody intersex?
Put simply, any notable divergence from perisex development is intersex.
In highscool you probably learned that XX chromosomes make a "female" and XY makes a "male". It's more complicated than that.
But there are all sorts of combinations you could have. There is XX, XY, XXX, XXY, XYY, XO.
You might even have a fragmentary autosome in your karyotype like me. Sometimes when a lot of data is missing the negative space will be filled by duplicating data from the intact autosome. Depending on what is missing and what is duplicated, sexual development can be significantly varied.
A difference in the production of sex hormones can make you intersex.
PCOS is intersex because high naturally occurring levels of androgens are not expected of a 46XX genotype. The elevated levels of these sex hormones cause the individual to develop associated seconday sex characteristics such as facial hair. More info in this link.
I have added a note to my post to address the oversight in not describing hypo-androgen PCOS as well. This post is about hyper-androgen PCOS
This is also true for people who's bodies do not produce sex hormones at effective levels. Pituitary hypo-productivity might be responsible, it might not, but if you couldn't start puberty without medical assistance then you're intersex.
Maybe you don't respond to some sex hormones. If you are 46XY with the associated expected hormone levels but are androgen insensitive, your development will not include the effects of those masculinising hormones. That makes you intersex.
There are too many examples to list, but this should give you the idea.
Genes and importantly how/if they are expressed is a factor too.
You might have a Karyotype of 46XX and have an expressed SRY gene/protein. This results in "masculine" fetal development and external genitalia, and is sometimes referred to as "XX male"
The inverse is also true, 46XY with an absent or suppressed SRY gene/protein results in "feminine" fetal development and external genitalia.
Again, this is a topic that could go on forever, but genetic elements that have caused sexual development that is different to the perisex expectation of sexual development makes you intersex.
Does being intersex make you transgender?
No. There are a lot of ways that intersex experiences intersect with trans experiences. And intersex people are absolutely justified in identifying with the trans label for any number of personal reasons. You can be intersex and trans.
Can I call myself intersex?
Nobody can decide to become intersex, it's one of those things that just is or isn't. But your doctor probably won't use the term intersex, it's not specific enough so they'll say Klinefelters or hypo- androgen or a thousand other things. So if you read this post and you go "hey, that's me" then go ahead and say "I'm intersex".
Perisex people are encouraged to share.
And a brief message to people who feel entitled to attack others for questioning their assumed perisex status. DON'T. You're not helping us, you're hurting us.
If somebody is saying "I think I might be intersex, I'm not sure" then they definitely have reasons for that. And you have no right to ask them, a person who is trying to make sense of their body, to defend themself when they have only just begun to understand it themself.
This especially goes for transmeds and TERFs. It's not your job to police this.