"Based" (corruption of base head - from someone who smokes base - street name for crack cocaine) was popular as an insult in rap / African American circles in the early 00s
Rapper Lil B got called it and decided on a whim to pretend the meaning was changed to mean something positive, started using it in this way, it caught on - mostly through the new York scene and its attendant twitter following
As all slang does in the last ~100-150 years, passed from black people to everyone.
Tough word to define. "Based" comes from black culture, if I recall correctly. To describe something as based means, essentially, "I see that you are strong in your convictions and I approve of your position", implying perhaps that a person's opinion is potentially controversial. It also could be, "You have strong views that align with my subculture."
I've seen "based" used to describe a lot of things in the last ten years. Teenagers describing their desire to overthrow the capitalist system. Ecologists feeling that we should ban cars and return to driving buggies. Neonazis acknowledging another's dogwhistle. Usually, people are based, not ideas themselves.
You think most social media is stupid and you think we should nuke the internet? That's pretty based.