Let me rephrase..
Continius power means that IF required by the components attached it will always supply that amount of power without cause or concern for the power supply.
Again, Components of a computer will only be supplied what they need no more.
Think of it this way.
The peak wattage of a power supply is very similar to someone maxing out the weight for a machine or exercise. They can do alot of weight, but only a few or one repetition.
Continious wattage is very much like lifting a paper clip or any weight that you have become used to. So much to the point that your not stressing yourself out. In this case it means the power supply can supply that amount of wattage with ease.