She wrung the towel out tightly.

Literal

She [topic-は] towel [object-を] firmly wrung.

絞る ('squeeze, wring, twist') is the verb for any twisting-extraction — wringing wet cloth, juicing fruit, narrowing focus (要点を絞る 'narrow down the key points'). Here it's the literal cloth-wringing sense. 固く is the adverbial form of the i-adjective 固い ('hard, firm, tight') — paired with 絞る it specifies the manner: not casually, but with effort. Wringing towels by hand is a classic everyday gesture in Japan, especially in households that use おしぼり (hot/cold wet towels handed to guests at restaurants) or wash floors with a 雑巾 (cleaning cloth).