The A ring is composed of several rooms. It has several storage rooms, the Brotherhood library and archives, the diner known as "The Den", and the council room (also refered to as Great Hall).
The library and archives store knowledge the Brotherhood has collected. Scribe Jameson also collects the holotags from fallen Brotherhood brothers and sisters.
The Lyons' Pride mostly spends their time in the room dubbed "The Den". It is distinctive from the other section of the Citadel, as it has more food than anywhere else. Here, Lyons' Pride members can relax and discuss tactics about defeating the super mutants and the Enclave.
The Great Hall is one of the most important buildings in the Citadel. Here, Elder Owyn Lyons discusses the situation with other paladins and knights.