"Du" is used when there would be no article in the English equivalent ("the woman eats meals") or when "some" would be used in English ("the woman eats some meals."). When "the" is used in English, indicating that we are talking about a specific meal, as is the case here ("the woman eats the meal"), just "le" is used, hence "la femme mange le repas." Hope that helps!
Oh, and just to further clarify (or confuse), in the negative construction when there would be no article in the English equivalent ("the woman doesn't eat meals"), you just use "de" in French ("la femme ne mange pas de repas"). Probably not something you need to worry about remembering at this stage, but just a heads up :)