Quick Answer: The p-value tells you the probability that your experimental results occurred entirely by random chance. In most sciences, a p-value of less than 0.05 (p < 0.05) is required to claim "statistical significance." It means there is less than a 5% probability the result was a fluke.
The Null Hypothesis
In statistics, you must start by assuming your theory is WRONG. This is called the "Null Hypothesis." For example, if you invent a new pill for headaches, the Null Hypothesis is: "This pill does absolutely nothing. Any effect is just random chance." The p-value is the tool used to destroy the Null Hypothesis.
How the P-Value Works
You run your clinical trial. Your pill cures 80% of headaches. A placebo cures 20%. You run the math and get a p-value of 0.01. This means: If the pill actually did nothing, there is only a 1% chance you would have seen such dramatically different results. Because 1% is so low (p < 0.05), you can reject the Null Hypothesis and declare victory.
The Danger of P-Hacking
If a p-value of 0.05 means a 1-in-20 chance of a fluke, what happens if researchers run 20 different random experiments? Statistically, one of them will show a "significant" result by pure luck. This is called p-hacking — torturing the data until a false positive emerges. It is a major cause of the "replication crisis" in modern science.