You probably identify as either a man or as a woman. Chances are, you were born with a corresponding set of "parts" (ie, a penis if you're a guy, a vagina if you're a girl). This is called being cisgender, and it means your sex (biological parts) matches up with you gender (what you see yourself as). Most people in the world are cisgender, like Barack Obama and Queen Elizabeth.

You've probably heard of being transgender (the "T" in LGBT). The "trans" category is pretty big, but the part of it you're familiar with is probably people who are either "MTF" or "FTM". These are people who were born as one sex (male or female) but feel like the opposite gender. For example, a trans woman is (typically) someone born with a penis and XY chromosomes who was (again typically) raised as a guy, but decided to transition and live as a woman. The opposite is true for trans men. Transitioning takes many forms (different clothing, hairstyles, makeup, all the way through hormone therapy and surgery). Trans people are a bigger umbrella though:

"Nonbinary" or "gender neutral" people exist outside of the man/woman gender binary. Sometimes they don't identify as either gender, sometimes as both, or sometimes as having no gender at all. Their sex (biology) is irrelevant (ie, they might have a penis or a vagina or be intersex). Often, nonbinary folks will go by a gender neutral pronoun. "They" is a common example. Even though it's typically used for a group of people, they can be a singular noun.

For example, let's say your coworkers is named Sam and uses "they" pronouns. If you were introducing them to someone, you'd say:

"Hey Sally, I'd like you to meet Sam. They are an accountant here. They're responsible for our budget. You'll love working with them"

The best thing to do is apologize to your coworker and ask what pronouns they use. Don't ask about how they were born, their "real" name, what genitals they have, etc. Just treat them like anyone else and you'll be fine.