This is the 9221st most frequent Russian word.
собачье
"Собачье" means "dog's" or "related to a dog" in English.
In this sentence, "собачье" refers to "dog-like" or "pertaining to dogs," emphasizing an attribute or possession associated with dogs.
Это собачье счастье.
This is a dog's happiness.
Here, "собачье" modifies "лаяние" (barking) to specify that it is the barking of a dog.
На улице слышно собачье лаяние.
Dog barking is heard on the street.
In this phrase, "собачьими" is an instrumental plural form of "собачье," describing races involving dogs.