Why is the Middle East such a big problem, and why do its troubles affect us as travelers and as ordinary citizens?
Long story. The main beef, of course, is between Israelis and Arabs. The Judaism vs. Islam picture isn't quite as clear-cut as it might seem. Although the conflict has a strong religious element, there are Christian and Muslim Israelis as well as Christian Arabs - the latter group being the largest of the minorities by some way. However, the conflict has its results in religious history.
It started in 70AD, when, following a Jewish revolt, the Romans effectively destroyed the then-province of Palestine. What followed was the diaspora - the dispersal of the Jewish population around Europe and North Africa, followed, centuries later, by large-scale Jewish emigration to the New World.
Following years of persecutions, which culminated in the Holocaust, the state of Israel was established in Palestine in 1947. There were and are very strong arguments for a Jewish homeland, but there is no denying that the establishment of Israel brought considerable suffering to many of the existing Arab residents of the area. Although it was originally envisaged by the founders of Israel and their backers in the West that Arabs and Jews would live side-by-side in the new state, many Arabs were literally forced from their homes. Others fled during the Arab-Israeli war that the birth of teh new country provoked in 1948. Estimates of how many Arabs were displaced, forcibly or otherwise, vary; the United Nations estimates it as 711,000.
This, along with religious tensions, Israeli expansionism and the Arab perception that Israel exists largely to execute US foreign policy by proxy in the Middle East, has led to the current situation.
The immediate effect of the conflict has been to drive up oil prices to very high levels, because, although Israel and Lebanon do not themselves have large oil reserves, trouble in one part of the Middle East usually leads to trouble in other parts. Those "other parts" supply most of the oil consumed by the West. When oil prices go up, western economies slow down - food prices can go up because it becomes more expensive to transport from factory to grocery store, companies have increased costs and people may lose their jobs.
Travelers, of course, have to pay more for airline fuel. At times like this, with the future price of oil uncertain, there's a lot to be said for buying air tickets well in advance.