It shows various signs of illness.

Literal

Illness [possessive-の] various signs [object-を] shows.

いろいろな徴候を示す — 徴候 (ちょうこう) means 'signs, symptoms' and is a formal medical term. いろいろな means 'various.' 示す means 'to show, to exhibit.' Written in a clinical, descriptive style.