The statement "Reject H0 if P < 0.01 " is called the decision rule. It always takes the form "Reject H0 if P < a" .
In any problem a is the probability that you are willing to accept in making the wrong decision: That is, rejecting H0 when you should not.
So, if a = 0.01 you are willing to take at most a 1% chance that you make the wrong decision. The p-value is the probability that you make a wrong decision in rejecting H0. So, if P < a the probability that you make the wrong decision is less than the probability you are willing to accept in making the wrong decision, meaning you reject H0.