The term iaijutsu (kanji: 居合術) means "the art of drawing a katana" in English. It is written いあいじゅつ in hiragana. It's pronounced roughly like "ee-eye-joot-sue".
Also known as battojutsu (抜刀術, literally the art of drawing a katana). Jutsu means way or skill. Iai can indicate the skill itself whereby the swordsman draws the katanaKATANA 刀 "sword" learn more... and cuts the opponent. The kanji for iai are used more frequently in the verb iawaseru (居合せる), which means “to be present” (for example, at the scene of an accident).
居, when used as the verb iru (居る, “to be”), is almost always written in hiragana (いる) because of its ubiquity. 合 is normally used as the verb au (合う), which means “to meet” or “to combine.” However, it refers only to the actions of impersonal forces, like the compounding of elements in chemistry. If you meet somebody, you would employ a different au (会う) to describe that meeting.
Note that 居合せる, 居る, 合う, and 会う are all given here in the infinitive form.