The term yakiire (kanji: 焼き入れ) means "quenching [in fire]" in English. It is written やきいれ in hiragana. It's pronounced roughly like "yocky-ear-eh".
When a sword is made in the traditional method, an important part of the forging process is putting the blade into a fire, which is what yakiire refers to. It’s also written in a slightly shorter form as 焼入れ. 焼き (yaki) means burning and may be familiar to non-Japanese in words like yakiniku (焼肉, grilled meat), yakitori (焼鳥, skewered grilled chicken), and okonomiyaki (お好み焼き, a fried cabbage and flour delicacy from the Kansai region).
The infinitive form of the verb is 焼く, yaku: “to burn, grill, fry, bake, roast.” The phrase 身を焼く (mi wo yaku, literally “to burn one’s body”) means to suffer pangs of love or jealousy. However, the more commonly used phrase is 身を焦がす (mi wo kogasu, literally “to singe one’s body”).
入れる, ireru, means “to put inside.” To refer to someone entering a room or building, one would use some form of 入る, hairu.