You're probably looking at the 8-10 year old range to truly understand the rules and begin to pick up strategy enough to play on their own. There is not much that is truly _secret_ in Catan, so it's an easy one where Dad/Mom can help guide the decision making. You could also very easily simplify the game - take out resource cards, take out bonuses for longest road / largest army, and reduce the winning VP to 5, then it's only about building settlements/cities and roads, and friendly trading.

There is even a junior version that says it is for ages 6+. I admittedly have never played it but have heard that it can work for some smart 4 year olds with a little guidance.