If you are in better physical condition you can do more work during a workout... The more work you do without exceeding your capacity to recover, the more you progress
If you are in better physical condition your vascular system is healthier and blood flow is more efficient... if you can send more blood to the muscles you can bring more nutrients in and get the training metabolites out; both of which will lead to easier growth
If you are in better physical condition you recover faster from a workout and can thus train more frequently... if you can train more frequently you progress at a faster rate.
Draw your own conclusion!