Higher education usually means anything after High School, which is also called Secondary Education. 'Tertiary education' (as Gary said) 'continuing education' and 'further education' are all synonymous with 'higher education'. These phrases imply university classes, but they are not limited to courses only for a four-year degree -- trade schools, vocational schools, etc can be included.

'Higher Education' can be a bit ambiguous - higher than what? Here in New Zealand - we use 'tertiary education' to mean any education after school, if that is what you mean.