There probably isn't a set definition to answer "What is a Country House?", particularly as each Country House will be different in some way. However, the following information gives an insight - both specific to Abercelyn Country House and also, in a general way, to other Country Houses.
As the name suggest you would expect to find a Country House to be an interesting building set in its own grounds. A Country House is normally the proprietor's home which is shared with guests. Unlike many hotels a Country House is not purpose built, therefore retaining its original character. Not all the services typically provided by a hotel are available, e.g. room service is generally not provided nor telephones in the bedrooms. On the other hand, there are aspects of a Country House which many guests appreciate, these include the personal attention of the owners, including suggestions for dining out or places to visit, rooms are individually furnished and decorated, and there are no charges for extras such as beverages.
You can expect a Country House to be an interesting building with history and set in its own grounds - Abercelyn Country House will not disappoint you.
Visit Wales summary definition is: Non-hotel style accommodation providing breakfast and evening meals by arrangement, situated in a quiet location, usually with it's own grounds. VisitWales no longer uses the grading designator "Country House" and therefore Abercelyn Country House is designated "Guest Accommodation".