She became happy.

Literal

She [topic-は] happy became.

幸福になる ('become happy') uses 幸福 as a na-adjective taking に before なる ('become'). The pattern [na-adjective]+に+なる is the standard way to express change of state into an adjectival condition. 幸福 ('happiness, well-being') is the slightly more formal Sino-Japanese counterpart of the native 幸せ; both translate as 'happy' but tune register differently. The verb なる ('become') is one of Japanese's most ubiquitous — change-of-state runs through everything from age to weather to emotion.