What does it mean when a girl you barely know sits next to you randomly when she sees you even though she is not in your class and there were extra seats available?

i think it means you're intrested in her.

for one, she might not have cared, sitting next to you on accident. Or she might be trying to get to know you.

go back, and if she does it agian, talk to her. if not, then it was never meant to be :(