Dogs can lick because of a variety of reasons. They lick themselves and their siblings to keep their fur clean. Mothers lick their puppies to clean them and stimulate urination or defecation. Older puppies and young individuals of wild canids lick mouths of adults as a greeting or request to vomit some food. Puppies eat this food until their mother's lactation ends and then start eating normal food. When puppies become older, licking becomes a way to great their siblings, when they come back. It also increases the degree of attachment between the puppies (members of the pack).
Licking is very common for home dogs. They tell us that they are happy to see their owner and want to strengthen the connection between them and us.
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