When something is described as higher, it's more advanced, difficult, or complex. Higher education is what you learn in college or graduate school, and it's more complicated than high school.
You're most likely to see the adjective higher being used to specify a type of education or schooling. Higher finance is likewise an area of banking or investing that's extremely complex because it involves enormous amounts of money. In Scotland, a Higher is a specific, high-level graduation certificate that qualifies students to enter a university.