This is the 15058th most frequent Russian word.
позволила
"Позволила" means "allowed" or "permitted" (feminine, past tense).
The word 'позволила' here means 'allowed' and is used to indicate permission given by 'Она' (she) to the students.
Она позволила ученикам использовать ее книги.
She allowed the students to use her books.
In this sentence, 'позволила' implies that life has given him the opportunity to achieve his dream.
Жизнь позволила ему осуществить мечту.
Life allowed him to fulfill his dream.
Here, 'позволила' is used in a reflexive sense to show that 'she' gave herself permission to do or indulge in something perceived as excessive.