The politics:

Before WWI, it had been a long time since Europeans had engaged in a drawn-out slugfest of a war. Wars had been reasonably short and sharp, generally won by the side that had prepared best.

That meant that each of the Great Powers (Germany, Russia, England, and France, and you could add Austria-Hungary and Italy if you were feeling generous and Turkey if you were on ecstasy) felt safest if they had an army that was ready to go at a moment's notice.

Of course, building such an army made the army's likely target feel unsafe, so that country would build an army, making the original power feel unsafe, and so on. So by the end of the 19th century you had an arms race.

France and Germany specifically didn't get along. And Germany's population, industry, and military power was increasing a lot faster than France's. So France allied with Russia, which also getting antsy about Germany.

Germany, in response, allied with Austria and Italy.

Britain, all this time, had kept aloof--they had a navy nobody could touch (so they didn't feel much threatened from the Continental powers) but their army was tiny (so the Continental powers didn't see them as a threat). Then Germany started building up its navy as well as its army. Britain responded, soon there was a naval arms race, and Britain, no longer feeling secure, joined France and Russia in their alliance.

By now it's the early twentieth century; every side is building weapons and finding new ways to set up their armies so that they can come into play quickly. That means less time from the decision to mobilize (to call the army up) to when the army is in combat. I read somewhere that the German army actually called up some units within Belgium (which was the easy road to France) to save time.

And nobody wants to be the second side to mobilize. So every time there's a diplomatic crisis, there's a danger that one side will mobilize, then the other will, at which point war will nearly be automatic.

Meanwhile, you had nationalist agitation in many places (Poles who didn't see why they should be Russian, Serbs who didn't think so many Serbs should be Austro-Hungarian subjects, and so on) and socialist agitation (people who thought that workers everywhere should take over because screw these outdated nation-states.) War is always a good way to paper over internal tensions, so many leaders weren't exactly against the idea of a quick, glorious war. (Because remember, they thought that modern wars were quick.)

Diplomats managed to defuse crises for a while, but then in 1914 a Serb killed the Austrian heir to the throne, Austria threatened Serbia, Russia threatened Austria, that involved both alliances (except that Italy decided "screw that" and stayed out for the nonce.) At that point, to stop the war one side would have basically had to stand down, and neither side did.