Cats usually snore when they feel comfortable and relaxed, but occasionally there could be a medical problem such as allergies or hairballs. A cat should be checked out by a veterinarian to rule out any physical ailments.
Just like humans, cats can snore from time-to-time. When a cat regularly snores loudly it shows that they are in a deep sleep and feel safe in their immediate environment. Occasionally cats can be affected by a medical problem, and if this is the case then this needs to be diagnosed. There is no cure for snoring cats, unless there is a respiratory issue, in which case a veterinarian can treat it.