There are British schools in Europe (some of which are covered on this website) and in other parts of the world (notably in USA, Canada and China). Some are affiliated to British organisations such as HMC, or international organisations such as ECIS (European Council of International Schools) or COBIS (Council of British Independent Schools).
Most offer the International Baccalaureate, some offer IGCSEs and A-levels, some a mixture of both systems. Sometimes they also offer the local qualifications (eg Spanish Baccalaureate) or prepare pupils for the American SATs (though this is more common in International schools, rather than British schools abroad).
Their atmosphere is generally very different from UK schools. Almost all were founded as co-educational schools; there is rarely a uniform nor formal structures such as houses and almost never prefects; there are usually a large number of nationalities represented among the pupils (especially in the main business communities); and leavers may be just as likely to go on to universities in Europe or the US as to UK universities. Because these schools cater for a transient population, parents can often be more involved than in the UK and the schools are necessarily flexible about the stage at which pupils join.
A number of UK schools have begun to tap the Asian market by establishing or franchising branches eg in Bangkok or Shanghai.