。
She doesn't want to speak in public.
Literal
She [topic-は] in-public [at-で] does-not-show-desire-to-speak.
The suffix ~たがる expresses a third person's desire as observed from the outside. Japanese grammar distinguishes between internal states (first-person ~たい, 'I want to') and externally observed behavior (third-person ~たがる, 'shows signs of wanting to'). Here, ~たがらない is the negative: she shows no inclination toward speaking in public. This internal/external distinction is one of Japanese grammar's most distinctive features.