Here is what we are doing, plain and simple. Most things in life are normally distributed, like take peoples heights for example. If we randomly sample 10 people, and the average of our sample is 7 feet the question is - is this sample statistically different from the whole population? The z-score converts the 7 feet height into a normal distributed curve - it is like a magical converter to make any number (height of people, speed of cars etc.,) into a common number that we can put on the bell-shaped curve. Once we convert or sample number onto the curve - we can see what percent of area are above and below the number on the curve and the probability of that number being significantly different.