Anything made of paper that you can blow your nose on such as tissue, toilet paper, paper towels etc.
My nose is dripping, hand me some booger paper, quick!
when you run out of tissue to blow your nose so you use a piece of paper. preferably lined. hence booger paper.
Bob: Shit we're out of klenex!
John: Its okay man just use some paper.
Tim: Haha. You mean booger paper :)