A sort of adjective/participle/verb phrase. To be "big on" something is to like it, be a fan of it, etc.
If you're a propenent of something, you're also big on it.
1) "I'm big on history. I really like learning about ancient people and how what they did affects us today."
2) "That congresswoman is really big on spending for schools and education."
enthusiastic about or placing emphasis on something
You have to be big on neatness to get a job at that company.