。
Her son is her reason for living.
Literal
She [topic-は] son [subject-が] reason-for-living is.
生きがい ('reason for living, purpose in life, raison d'être') is one of the celebrated 'untranslatable' Japanese words — the personal anchor that makes life feel worthwhile. Here the structure is the standard double-subject [topic]は[subject]がX construction, with 生きがい as the predicate noun. ~が生きがいです reads as a fond declaration of what makes life worthwhile — common with hobbies, work, art, or loved ones.