When Jesus used story to illustrate what was happening in His own ministry in Luke 15, it was a story that really summarizes the entire narrative of the Bible. To begin with in the three parables of Luke 15 something of great value exists. The shepherd of the first parable places enough value on the one lost sheep to go and search for it, the woman places a important value on the lost coin in the second parable, and climatically the father in the third parable loves the son immensely.
Similarly as we look at the Bible as a whole something of great value exists to God, His creation. In the opening scenes of Genesis, God speaks His creation into being commenting on each day that it was "good" but after the creation of male and female he says His creation is "very good" in chapter 1:31. God Himself delights in humanity, and it is evident that He delights in His entire creation as we see the beautiful diversity of the animal and plant life in this world. In Proverbs chapter 8 "wisdom" is poetically spoken of as being along side God in creation as a "craftsman" and in verse 31 it says "rejoicing in His whole world and delighting in mankind".
God places an infinite value on His creation. We read of Him interacting with humanity and inhabiting His creation in Genesis 3:8, He is walking in the garden in the cool of the day.
So as Jesus begins His story of redemption in Luke 15, He establishes that God delights in His creation as the father loves his son in the parable and the "sinners" that He is going to and "eating with" are a part of that creation.