。
She is proud of her students.
Literal
She [topic-は] her own students [object-を] is-boasting-about.
自慢する with the progressive ~ている describes an ongoing attitude of pride or active boasting — context decides between 'is currently bragging' and 'has the habit of boasting.' 自分の生徒たち ('her own students') uses ~たち to pluralize, since 生徒 alone is ambiguous between singular and plural. Notable that 自慢 has a faintly negative undertone in Japanese (boastfulness can be unseemly), but applied to students or family it reads as warm pride.