This is the 7037th most frequent Russian word.
барских
The word "барских" is the genitive plural form of "барский," which means "of barin" (relating to a nobleman or landlord).
Here, 'барских' is used as an adjective in plural genitive case derived from 'барский', meaning 'of a lord' or 'lordly', modifying 'владениях' (estates).
Мы гуляли по барских владениях.
We walked through the lordly estates.
In this sentence, 'барских' modifies 'традиций' (traditions) in plural genitive case, indicating traditions associated with lords.
Барских традиций придерживались в этом доме.
The traditions of the landlords were upheld in this house.
Here, 'барских' is an attributive adjective in plural genitive case describing 'вещей' (items), denoting items related to lords.