Cat Breath is a recurring joke found within the Heathcliff comic strip. With very few exceptions, any reference to "cat breath" refers to the breath of Heathcliff himself (as opposed to, for example, his father or girlfriend)
Cat Breath is presumably a result of the diet kept by Heathcliff, which can vary from gourmet human foods to stereotypical foods eaten by cats such as birds and fish . Heathcliff's Cat Breath, judging from the reactions displayed by the characters around him, is associated with a particularly noxious smell.
Most strips involving Cat Breath feature the mice who live in Heathcliff's home. The vast majority feature Heathcliff, mouth agape, breathing into the hole of the mice. The mice, inconvenienced by the smell of Heathcliff's Cat Breath, will most often remark on the situation in a sardonic manner. It should be noted that these strips are a separate entity from other strips that involve Heathcliff's opened mouth being inserted into the homes of the mice, which do not involve Cat Breath.
While Cat Breath is often held to be a powerful weapon in the Heathcliff universe, it has been shown that Heathcliff himself is weak against the phenomenon of dog breath, a similar entity that is emitted from dogs, not cats.