。
She did the housework diligently.
Literal
She [topic-は] housework [object-を] diligently did.
せっせと is one of Japanese's beloved 擬態語 (state mimetics), describing a manner of busy, diligent, energetic activity — bustling about, working away. The と attached is the adverbial と often paired with mimetics to attach them to verbs (バタンと, ゆっくりと, きっぱりと). The whole phrase 家事をせっせとした paints a vivid picture of bustling domestic activity. State mimetics are one of the great pleasures of Japanese vocabulary — there are dozens for different shades of activity, mood, and physical state.