Adjacent rooms are hotel rooms that are next to each other, most likely side by side.
A party of guests might request adjoining rooms to ensure that they are situated in the hotel in close proximity to each other. Guests should remember that adjacent rooms does not necessarily mean that they are adjoining rooms.
Some hotels consider adjacent rooms to be simply near each other, such as across the hall. This is not technically the definition of adjacent rooms, but most likely due to the fact that the room numbers are adjacent (odd numbers on one side, even numbers across the hallway).
For more, see this post: Adjacent Rooms vs Adjoining Rooms.