In Japanese, the word rōmaji (ローマ字, lit. Roman characters) broadly refers to the Roman alphabet.
In English, the word is usually used to refer specifically to the writing of the Japanese language in Roman characters as opposed to the usual mix of kanji and kana.
Japanese may be written in Romaji for many reasons: street signs for visiting foreigners; transcription of personal, company, or place names to be used in another language context; dictionaries and textbooks for learners of the language; or even simply for typographic emphasis.
There are a number of different romanization systems in use: the four main ones are Hepburn, Kunrei-shiki, JSL, and Nippon-shiki. Hepburn is the most widely accepted method outside Japan, and is used on Japanese road signs and passports. The Japanese government, however, officially sanctions Kunrei for use in education.