The term iaido (kanji: 居合道) means "art of drawing a sword" in English. It is written いあいどう in hiragana. It may also be rendered in English as iaidō or iaidou. It's pronounced roughly like "ee-eye-doe".
This art of drawing the sword can also be referred to as simply iai. Iai is composed of the kanji for being and meeting. “To be” would be iru, 居る, and “to meet” would be au, 合う. The former is almost always written out in hiragana, いる, because of its ubiquity.
合う cannot refer to meetings between people (for that, a different au, 会う, is used). It describes the meeting of impersonal forces or abstractions and so is used in the Japanese words for things like fusion, synthesis, and combination.
道, in isolation, is pronounced michi: road, path, way. Iaido refers to the art, whereas iaijutsuIAIJUTSU 居合術 "the art of drawing a katana" learn more... (居合術) refers to the technique practiced within the art.