It is very simple- they are synonyms. They mean almost exactly the same thing and they are interchangeable. I hope this helps.

I agree with Cory to an extent. Both urgent and pressing are virtually identical. Although, if something is urgent, it can have a sense that the consequences are more dire if the issue is not address, while pressing still indicates that something needs to be addressed as soon as possible, if it isn't, the consequences, might not be as severe. For example, if someone is dying and in need of medication, that would be considered urgent; whereas "pressing" might be a more apt description of someone who is is coming up on a deadline for an assignment. However, depending on how strongly you feel about the importance of getting a good grade on the assignment, you could use urgent too, and it would sound perfectly natural to a native English speaker. To say that the need for medication in the first scenario, however, it might sound a bit awkward. I think using pressing to describe something that needs immediate attention sounds more awkward that using urgent to describe something not quite as dire. In the context of the text you are trying to understand, the second sentence only serves to reinforce the first. Both sentences could easily be replaced by "The need for food and water is one of the most urgent problems facing this country" and it would mean the same thing as the first sentence.

I feel like there isn't much of a difference between the two words most of the time. I would say that if something is urgent then it needs to be dealt with right away, but a pressing problem isn't necessarily urgent. A pressing problem can mean one that is important and needs to be dealt with soon, but it might not have to be dealt with right away. An "urgent need for food and water" seems like people going to die soon if the problem isn't fixed quickly, so it needs to be fixed right away. A "pressing need for food and water in this country" seems like the problem is very important and needs to be dealt with soon, but it doesn't necessarily have to be right away. Maybe there are just a lot of people going hungry, but maybe aren't to the point of starving to death yet.