Ruth was considered a dog to the Jewish people because of her heritage. She wasn't Jewish, but was a Moabite. But she married into a Jewish family, and was therefore welcomed into the Jewish commonwealth and because part of the family of God.
God had made a covenant through Abraham that extended to all of the Jewish people. He blessed them as a people, and He blessed them with a place.
With Christ, the covenant was expanded and God allowed anyone to be welcomed into the family and fall under the promises of God. And we're the same as Ruth. We're dogs, unclean, and unworthy. We are outside the covenant of Grace and we didn't have a redeemer.
But praise God that we can be welcomed into the family of God through Jesus Christ!