The term togi (kanji: 研ぎ) means "sharpening/polishing" in English. It is written とぎ in hiragana. It's pronounced roughly like "toe-ghee", rhyming with the word "hoagie".
Can refer to either sharpening or polishing. 研ぐ, togu, “to sharpen or polish,” can also be used in relation to sharpening a pencil, sharpening a knife, or washing rice (though for the latter, a different kanji, 磨ぐ, is often used).
There are two parts to the 研ぎ process when making a sword: shitaji togi (下地砥ぎ) and shiage togi (仕上げ砥ぎ). 下地 (literally, “the ground below”) means foundation. 仕上げ can refer to the act of completion, the final stage of completion, or the thing itself that is completed.