Some dude hates new stuff and finds the old stuff alwaysbetter no matter what, especially in rap.
Person:'' Yo, Post Malone's new album is dummy lit.''
Other person: '' Wtf you listen to post Malone, he is shit, nowadays hipster liberals always listen to crap music''
Person: ''Oh yeah, I forgot that the Oldschool police was patrolling today'.'
Someone oldschool is someone acting cool and casual, bombing newbies on it's way, and always doing what he can to get a good time with his real buddies.
oldschool burn is a term referring to a classic cut-down, or a cliche that is directed towards a particular person to show a superiority over said person.
"How you like dem apples?"
"Dang bro, that was an oldschool burn!"