This is the 3361st most frequent Russian word.
позволяли
"Allowed" or "permitted" (past tense, plural).
In this sentence, 'позволяли' is used in the imperfective past tense indicating a repeated action of allowing access to the library.
Они позволяли нам пользоваться библиотекой вечером.
They allowed us to use the library in the evening.
Here, 'позволяли' signifies the possibility or permission provided by benefits, emphasizing an enabling condition during the past.
Льготы позволяли многим студентам учиться бесплатно.
The benefits allowed many students to study for free.
In this sentence, 'позволяли' expresses the facilitation or permission extended by the new laws.