The quick and dirty explanation, as I've always understood it, is that trans means the genitalia you were born with does not match up to your perceived gender. A transman may have a vagina, but everything in his head tells him "I AM a guy, my body just got it wrong."
It doesn't necessarily have to be genitalia either, since many trans people don't actually go through with "bottom surgery."
That's why I added the last part. Lots of transmen will have vaginas for the rest of their lives, it doesn't mean they aren't men. And lots of transwomen will always have their penis, but it doesn't make them any less a woman.
Also, highlight.
I guess a lot of my confusion comes from not really knowing any (at least, openly/as far as I know) trans people in person. I mean, what does it mean practically? I guess part of my confusion comes from blurred gender lines and gender roles.
About all I really seem to understand from my rather limited interaction with trans people is that it often seems to involve preferred physical appearance and preferred bathroom usage. I'm not sure if there's something that's more basic that I'm not grasping. Like I said though, I guess I have a hard time not viewing gender itself as a social construct with a blurred line separating things.
I suppose that what I'm saying is "the quick and dirty answer" only gives me a vague understanding. Probably just my human brain trying to put some kind of concrete/solid characteristic to what being trans means. Like I said though, even with a definition I feel like my understanding is poor.
To put it another way, could a trans person do something that makes them not "truly" trans? If so, what?