In Layman's terms:
Hypothesis test is where you have a current state (null hypothesis) and an alternative state (alternative hypothesis). You assess the results of both of the states and see some differences. You want to decide whether the difference is due to the alternative approach or not.
You use the p-value to decide this, where the p-value is the likelihood of getting the same results the alternative approach achieved if you keep using the existing approach. It's the probability to find the result in the gaussian distribution of the results you may get from the existing approach.
The rule of thumb is to reject the null hypothesis if the p-value < 0.05, which means that the probability to get these results from the existing approach is <95%. But this % changes according to task and domain.
To explain the hypothesis testing in Layman's term with an example, suppose we have two drugs A and B, and we want to determine whether these two drugs are the same or different. This idea of trying to determine whether the drugs are the same or different is called hypothesis testing. The null hypothesis is that the drugs are the same, and the p-value helps us decide whether we should reject the null hypothesis or not.
p-values are numbers between 0 and 1, and in this particular case, it helps us to quantify how confident we should be to conclude that drug A is different from drug B. The closer the p-value is to 0, the more confident we are that the drugs A and B are different.
