I have tried my soaps from their baby stage -- just safely saponified -- through well over a year old.
When young, the soaps "melt away" faster in the shower. The lather is often acceptable, but not as good as it is later on. If you split open a bar that has been colored with something like cocoa, you'll see a dark brown layer of color around the outside surfaces of the bar, but the inside of the bar is still pale brown. This indicates there is much more moisture in the center of the bar that needs to evaporate.
When just cured -- about 4-6 weeks old -- I see the lather begin to improve. It takes less work and less water to build a good suds. A bar colored with cocoa will show a color change throughout most of the inside of the bar, although the very center may still be pale, indicating there is still moisture in the center of the bar that has yet to migrate out and evaporate.
Around that time or a few weeks later, I notice another odd change... the bars begin to vibrate when tapped. What I mean is this -- if you gently tap two young bars together, they will obviously hit together, but they won't bounce away. This is what a physics teacher would call an "inelastic collision". Gently tap the same 2 bars at age 6-8 weeks, and you'll feel a slight vibration with your fingertips and get a slight sense of bounciness (elasticity). This is telling me the crystalline structure of the soap is gradually becoming more organized and stable.
After about a year, soaps that did not lather especially well when young will now lather much, much better.