Because of sin, man lost his inheritance in the Garden of Eden, which is a land of promise flowing with milk and honey. There, Adam and Eve enjoyed God's blessing and rest, with a promise of eternal life. They lose their place in the Garden of Eden, the consequences are suffering and pain to all humans that will follow after them.
God's promise to His covenant people is to take them to a land flowing with milk and honey, a land of abundance and not a land of sorrow and suffering; not a land of bondage, slavery, and affliction. The promised land is a land where God rules as King.
The kingdom of God is His dominion as king over His people; to the Israelites of old, they live by the laws and commandments of God, today we live by faith in the word of God in this Kingdom.
The promise of God to Abraham is the promise of God to all that follow God the way Abraham followed God, by faith. The promise to His people is real today just as it was yesterday; whatever God said concerning His children yesterday, He is also saying to His children today.