The scientific method tests hypotheses. We don't actually prove our hypothesis, we set out to disprove the opposite (called the null hypothesis). And we don't even get to actually disprove the the null hypothesis either; the best we can manage is to say that the probability of the null hypothesis being right is very low.

How low is very low?

Well, that is in the eye of the beholder: and the beholder sets this level by defining the alpha threshold.

In medicine, for historical and arbitrary reasons, we set alpha to be 0.05. That is, we are willing to accept the a 5% chance of a false positive study result, aka Type I error.

If the p-value of a study is below alpha (p < 0.05, typically), the study results are said to be statistically significant.

In some cases, it may make sense to set alpha even lower than 0.05; but that of course increases the risk of failing to reject a false null hypothesis Type II error. As in many situations in clinical medicine, setting alpha is a compromise. One cannot 'err on the side of caution' with a uniformly high or low threshold. The conservative approach depends on the clinical details