Subtracting numbers is just the same as adding them, only walking the other way along the number line. To subtract 3 from 8, you start on the number line at 8, and walk backward three steps until you get to 5 - that's the answer: 8 - 3 = 5. Subtraction tells you how many cookies you would have left, if you started with eight cookies and then you gave three of them to your best friend.
You can also think of subtracting numbers as being the same as adding a negative number. If you added 8 + (-3), you would also get 5. Why is this true? Because 8 + (-3) is the same thing as -3 + 8, because addition is commutative. And -3 + 8 means that you should start on the number line at -3, and walk forward eight steps until you get to 5, and that's the answer.
Bibliography and further reading about subtraction: