To understand the p-value, we need to understand the context. In this specific case, the context is hypothesis testing.
The phrase hypothesis testing seems to be intuitively understood by anyone. You are trying to prove something, and you define your hypothesis. However, as you conduct the tests, this hypothesis is defined in a bit more convoluted way.
This tutorial will outline the hypothesis testing procedure, and refresh your knowledge of how the tests are usually conducted using the z-critical and z-calculated values. We will then proceed to show how the p-value is related to this procedure and how today it is used as a single random error metric. We will also indicate what potential mistakes are made if this concept is not properly understood.
A pdf version of this tutorial is available here.