Decision Rule vs Significance Level

Fixing the rule in advance is what keeps a test honest, because $\alpha$ (alpha, the significance level) is the probability of rejecting a true null hypothesis and must not be adjusted once you see the result. The AP version is a direct comparison: if the p-value is at or below alpha you reject $H_0$ and conclude there is convincing evidence for the alternative, and otherwise you fail to reject. For example, at $\alpha = 0.05$ a p-value of 0.032 leads you to reject, while a p-value of 0.080 does not. You never accept the null hypothesis, since failing to find evidence against a claim is not evidence that the claim is true.

The significance level, written $\alpha$ (the Greek letter alpha), is the line you draw in advance for how much evidence counts as convincing. If the p-value is at or below $\alpha$ you reject the null hypothesis; if it is above, you fail to reject. For example, with $\alpha = 0.05$ you reject when the p-value is 0.05 or less. Because $\alpha$ is also the long-run rate of falsely rejecting a true null hypothesis, a smaller $\alpha$ such as 0.01 demands stronger evidence.