In more detail
A test assumes a null hypothesis ("no effect", "the coin is fair"), computes a statistic from the data and asks how often a result at least that extreme would occur if the null were true. A two-sided test counts extremes in both directions. A z of 2 gives a two-sided p of 0.0455 and a z of 1.96 gives 0.05, the usual threshold. A small p suggests the data are unlikely under "no effect" but says nothing about the size or importance of the effect.
Why it matters
p-values drive decisions in medicine, A/B testing and science, and they are widely misread. p = 0.03 does not mean a 3% chance the result is a fluke or a 97% chance it is real. Running many tests inflates false positives: with 20 independent tests of true null hypotheses at the 0.05 level, the chance of at least one "significant" result is 1 − 0.95²⁰ = 64%.
Example
A coin lands heads 60 times in 100 tosses:
normal approximation z = (60 − 50) / 5 = 2.0 → p = 0.0455
exact binomial test P(≥ 60 or ≤ 40 heads) → p = 0.0569
The approximation says "significant at 0.05"; the exact calculation does not. A result this close to the threshold is weak evidence either way.
Common confusion
A Confidence interval carries more information: a 95% interval that excludes the "no effect" value matches p < 0.05 for the same test, and it also shows how big the effect might be.