Hume's Fork

I think you were right that the text book makes this much more difficult than it needs to be.

I'll try to keep it simple. (Not one of my strong areas, I know)

The point of the fork is to keep separate the two kinds of statements we can make about the world. 

The first kind, 'Relations of Ideas' are things like  "2 + 2 = 4", "all bachelors are unmarried", and truths of geometry, mathematics and logic.

These kind of ideas have certainty, but according to Hume, tell us nothing about the world. It is as if they are sealed off from the 'physical' world. The logical 'purity' of these ideas, and therefore their certainty, either cannot transfer to the real world, (as in the application of geometry and maths to the construction of bridges that are perfect in 'theory' but collapse in the 'real' world), or tell us nothing, like a bachelor telling you "Hello, I'm a bachellor, I'm not married!" 

The second kind 'Matters of Fact' are statements like, "flowers bloom in the spring",  "the Earth has precisely one moon", and "water freezes at 32 degrees Fahrenheit". These kind of statements are based on our experience and observation of the world. They cannot have the kind of certainty that 'relations of ideas' have because:

1. we use our senses to get the information (and we know how dodgy they are!)

2. we can never be certain that the behaviour of these things won't change. (We might be very, very confident that it won't change, but we cannot have logical certainty about it.) 

Hume's purpose was to show that science, cannot bring these two kinds of statements together however much it wants to. It can say very useful things about the physical world based on it's experiments and observations, and it can describe the various physical phenomena in terms of logic, maths & geometry, but that certainty will never be in those phenomena themselves. 

I think that's rather brilliant. But, of course, I may be wrong. 

If that's not enough for you then see Wikipedia which is excellent on this http://en.wikipedia.org/wiki/Hume's_fork