The following explanation is taken almost verbatim from Wikipedia at http://en.wikipedia.org/wiki/Further_education

“Further education is a term mainly used in connection with education in the United Kingdom and the Republic of Ireland. It is post-compulsory education (in addition to that received at secondary school), that is distinct from the education offered in universities (higher education). It may be at any level above compulsory education, from basic training to Higher National Diploma or Foundation Degree.

A distinction is usually made between FE and higher education (“HE”) which is education at a higher level than secondary school, usually provided in distinct institutions such as universities. FE in the United Kingdom therefore includes education for people over 16, usually excluding universities. It is primarily taught in FE colleges, work-based learning, and adult and community learning institutions. This includes post-16 courses similar to those taught at schools and sub-degree courses similar to those taught at higher education (HE) colleges (which also teach degree-level courses) and at some universities.”

I would just add that the term FE also includes A Levels, which is the British equivalent of the Austrian matura.