There are certain foods which are toxic and essentially poisonous for cats to ingest, such as walnuts. If you have a cat it is highly recommended that you avoid feeding them any type of nuts whatsoever, including walnuts. Feeding your cats walnuts can lead to all sorts of health problems, such as an upset stomach, diarrhea, and even seizures in some rare cases.
The primary reason why walnuts are dangerous for cats to ingest is because they contain phosphorus so you should therefore avoid feeding them to your cats altogether. Walnuts are also considered to be poisonous for dogs and most other animals.