Far East (in contrast to Middle East) refers to countries/territories of East Asia e.g. China, Japan, the two "Koreas", Hong Kong, Taiwan etc. However, Southeast Asia region is usually added to be considered as such Far East too, some Southeast Asian states are Malaysia, Singapore, Thailand, Indonesia. Hence Far East means East Asia (sometimes plus Southeast Asia). Nevertheless, the Far East is still a vague term with no definite boundaries. Sometimes it is defined as anywhere in Asia "more eastward" than India.
Many of the cities of the region designated as the Far East are amongst the most crowded and overpopulated in the world.
Far East seems to be a term coined and used more frequently by the British and other Europeans and had its origin since their colonial era in East Asia. It was seen as literally very "far" from a European point of view. The term Far East is often seen as a Eurocentric one nowadays.