From earliest history, there has been conflict between people who live upriver and people who live downriver. Someone upriver has the power to seize control of the water supply which is generally the lifeblood of the people further down from them. Survival means that the people downriver must get effective control over their supply, whether it be by treaty, by conquering the people upriver from them, or by being conquered by the people upriver.
Where I live, in California, we are experiencing a slow version of this, as systems of water rights developed over a century ago, when the distribution of both water and people was extremely different, are falling apart under the strains of a worst-in-a-millennium drought. But the situation in the Nile Valley is even worse.
Several things contribute to this. The first is the simple growth of population: Egypt now has 82 million people, Sudan 38, and Ethiopia has grown to a full 96 million. To understand this properly, you need to realize that the borders of Egypt shown on a map are almost complete nonsense: Egypt consists of a narrow Nile Valley, ranging from tens of miles wide at its northern reaches to narrow enough that someone strong enough could throw a frisbee across it at its narrowest, in which the entire population lives, along with all the agriculture and industry; beyond that narrow valley is open desert, home primarily to sand dunes and the occasional scorpion. This part of the world is the Nile Valley.
The second complex issue is the Aswan Dam. When Gamal Abdel Nasser came to power after overthrowing the monarchy, one of his first promises was to build a tremendous hydroelectric dam to provide the electricity which would modernize the country. As part of trying to get international loans to fund its building, countries asked for feasibility studies; those studies all came back saying that the dam was a terrible idea, as it would interrupt the regular cycle of flooding of the Nile which is the foundation of the richness of the Nile Valley's soil. The dam would work fine for a few years, at which point the soil would start to die, the desert would encroach, and the country would starve to death. Nobody wanted to fund this.
But Nasser had made promises, and he needed to keep them, so he sought funding from "alternate sources" -- that is, the Soviet Union, who was quite happy to fund this and get Egypt in their pocket. ("Fund" ended up meaning that Soviet engineers showed up and built everything and then left, incidentally, leading to almost no technology or skills transfer -- but that's another story) And things unfolded almost exactly the way the analyses said: Egypt now had electricity, but its farmland has been steadily collapsing, the desert encroaching and the valley getting narrower.
This collapse of life along most of the length of the valley has led to almost unimaginable desperation, and to tens of millions of people flooding into the cities of Cairo and Alexandria hoping for a chance at a better job -- leading to some of the most extraordinary slums you have ever seen (did you know that it's possible to build a ten-story high mud hut? The trick is to build a frame of cement and rebar, and then use mud-brick walls for the rest. No windows; the walls aren't sturdy enough to support that) and even more extraordinary unemployment, which was one of the key things that led to the revolutions of the Arab Spring, the subsequent political rise and fall of the Muslim Brotherhood, and our latest Egyptian dictatorship.
But the pressure from collapsing agriculture is extremely keenly felt: the government's single largest annual expense is the wheat import which it uses to keep bread cheap enough to avoid mass starvation. Political upheavals in Egypt tend to happen, like clockwork, a few months after something interferes with the wheat harvest. (The original revolution which toppled Mubarak, for example, happened after Russia closed off its entire foreign wheat sales, after a serious drought led to major crop failures in Russia and Ukraine.) You may notice that, as the climate continues to change, wheat harvests become increasingly unpredictable.
Further South, Sudan hasn't been politically strong enough to try to wrest control of anything from Egypt since the Assyrians conquered Upper Egypt. But Ethiopia is a different matter: the highland empire has been a political power in Eastern Africa for millennia. As its population rises and it finds itself no longer quite as distracted by the chaos which has overwhelmed it for decades (famines and wars, mostly: the rains in Ethiopia are notoriously unreliable), it has gotten some very different ideas about just how Nile water should be allocated from what its neighbors downstream have historically gotten out of it.
This ascent of Ethiopian power in the Nile Valley is important and worth watching. Egypt and Sudan will keep negotiating with it, but their political power is not at its strongest right now, and it's quite possible that this could pass a "critical threshold" beyond which they can no longer really hold back Ethiopian power, at which point Ethiopia may take more of the Nile's resources for itself, further weakening Egypt and Sudan.
But at the end of the day, the problems are very fundamental:
There are nearly 220 million people living in the Nile's watershed, and it's not at all clear that the Nile has enough water to support them.
None of the powers along the valley are in strong enough shape to make huge infrastructural investments to increase efficiency. They might be able to make some.
This water is critical for everything from electricity, to irrigation, to soil fertilization, to simply drinking it, as well as holding back the desert.
Any failure of this water system can therefore have catastrophic human and political consequences.
Political problems in the Nile Valley can spread out along several significant axes. Because of the Suez Canal, Egypt and East Africa have strategic control over sea traffic through the Red Sea, and one of the key transport routes between Europe and Asia. (cf the effect that Somali piracy was having on sea traffic there) Egypt is by far the most populous Arab state, and its cultural and media influence is tremendous: Cairo is the Hollywood of the Arabic language. It's also the gateway between the Middle East and North Africa, and North Africa has a range of influences on Europe, being after all neighbors across the Mediterranean Sea. (Lots of people leaving North Africa would, for example, mean lots of North Africans arriving in Europe)
So this is a situation well worth paying attention to over the next decade: the availability of water, electricity, and agriculture in the Nile Valley, and the political struggles between players along the river, will be a major factor shaping our world, especially the band going from East Africa, up through the Middle East, into North Africa and Europe, in years to come.