According to Hume, causality cannot be found in "things themselves", nor can it be empirically accessible. Instead, it is we, the observers, who attach causal relations among things merely because we constantly see them occurring together, i.e. merely due to Habit.
Kant was convinced by Hume's argument that causality is not an inherent feature of things themselves. However, he deeply refused to accept that it is only a matter of habit, and, in order to "escape" out of the conundrum, was forced to create an entire new (and quite fruitful) field of philosophy. The fact that he had to do that much stretching and make his famous "Copernican Turn" in order to "solve the problem" just goes to show how much Hume's position bothered him.
Now, the question is: why was Kant so bothered about causality being merely a habit? What consequences did Kant see in Hume's statement that forced him to revolutionise philosophy just to refute it? Surely we can still have knowledge and science even if we say that causality is not valid a priori, no?
EDIT: After giving some more thought to this, I start to get the gist of how problematic Hume's position can be for science.
A key step in advancing our knowledge is when an observation is made that contradicts our current theory. The scientist then has two choices:
1) Assume causality holds, and immediately look for causes of this discrepancy. Because of the Principle of Uniformity, one has to assume that this phenomenon has always been present in Nature, but it was simply neglected by our previous theory. The new theory then has to explain how the previous one worked so well, even without taking these phenomena into account. I.e. the previous theory must somehow be "included" in the new theory. This necessarily leads to a broadening of our understanding and of our control over the world.
2) Take a skeptical position about causality, which means these new observations can be merely a consequence of causality breakdown, and we can say nothing more about them. Our previous theories remain correct to the best of what we can possibly say. Whenever they are contradicted by experiments, we have nothing to do but to frustratingly accept that Nature can play tricks on us.
The Humean viewpoint does not even allow to investigate a cause of this purported breakdown in causality: one really can say nothing about it.
Of course, even a partisan of Hume's side can take position (1) "for practical purposes", but by doing so he is admitting that one needs to assume causality a priori in order to have knowledge of the world.
In conclusion, in order to at least have the possibility of knowledge, one has to take the standpoint that the world is necessarily logical.