。
She has a cast on her arm.
Literal
She [topic-は] arm [on-に] cast [object-を] is-fitting.
ギブス is a loanword from German 'Gips' (plaster), not English — a legacy of Germany's major influence on Japanese medical education in the Meiji era. Many Japanese medical terms derive from German. はめる means 'to fit on, put on' something that wraps around or encases. The ている marks the resulting state.