Small number = Big Opening = Allows in more light = Less time required for correct exposure = shallow depth of field.
Big number = Small Opening = Reduces amount of light in = More time required for the same exposure = wider depth of field.
Depth of field is the distance, or depth, of your picture that will be in focus.
In summary...as nice as it is to understand what the camera and the lens are actually doing (the lens opening, focal points, amount of light, yada, yada, yada) I'm going to focus on what I need to remember at that moment to get the desired photo:
Small Number = Small amount in focus
Big Number = Big amount in focus
Now it's time to go play :)