Romaji is Japanese words written in the Roman alphabet. It is seldom used in media, unless for the purpose of educating in the Japanese language or other special purposes. Sometimes used to explain, expound or guide in Kanji/Kana usage.
For Danbooru purposes, the tag refers to instances of Japanese text written in Latin alphabet where Japanese characters would normally be expected. Thus character names, trademarks etc. don't warrant the tag, even if technically they contain romanised Japanese text. Any piece of dialogue, however, as well as sound effects and similar elements which would normally be expected to be understood by Japanese speakers, but are for whatever reason rendered romanised, do qualify.