In a hypothesis test, if the computed p-value is less than 0.001, there is very strong evidence to

reject the null hypothesis

Explanation:

If the p-value is smaller than the significance level alpha, then we reject the null. You can think of the p-value being the probability that the null is correct. If the p-value is below a certain threshold (the significance level), then we can be fairly confident that rejecting the null is a good decision.

Your teacher or textbook might have brought up the phrase "If the p-value is low, then the null must go" as a way to help remember this rule. If the alpha level isn't stated, then usually it defaults to 0.05

power property.

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