I mean that the heir, as long as he is a child, is no different from a slave, though he is the owner of everything,Galatians 4:1 (ESV)
The modern western world does not emphasize the role of heirs as previous generation did. In the first century of the Roman world, the wealthy and powerful would pass on their status to their children especially to the first born male of the household. However, there was no status in the household afforded to the children. They no different in status that the slafes of the household though he would eventually inherit all that belonged to his father.
In the Galatian context, Paul illustrates that God’s previous revelation of the Law given through Moses was to train the nation of Israel. The nation needed a tutor to instruct them on the nature of God; specifically his rightousness and how that righteousness translates into personal relationships between the individual and God and between the individual and others.
Just as the child of the master would mature and become the inheritor and master of the hoursehold, the people of God go from needing the Law to needing the savior who fulfilled the requirements of the Law.