WWI was, to vastly oversimplify it, a squabble between the 6 most powerful European empires at the time (Britain, France, Germany, Austria-Hungary, Russia, and the Ottomans) over what the balance of power should be in Europe and, by extension, the rest of the world. There were various points of tension such as:

• Britain held pretty much complete dominance over the oceans at the time (Britania rules the waves and all that) because of the vast navy they'd built to secure their colonial empire. Germany, an up and coming superpower, wanted to break this control by building up their own Navy to match the British, which led to a naval arms race between the two countries.
• France resented losing Alsace-Lorraine, a border region between France and Germany, to the German Empire 40 years ago. For various historical and cultural reasons the territory was an important part of both German and French nationalism, so whomever held it essentially one-upped the other and France was itching for a fight to get it back.
• Austria-Hungary and Russia were competing domination of the Balkans, which Austria-Hungary viewed as part of their geographic sphere of influence while Russia saw itself as protector of the Orthodox Slav population. Austria-Hungary annexed Bosnia in 1908 which annoyed Russia, and Germany backed Austria-Hungary in a joint stance against Russian influence in Central Europe. Along with Italy this formed the Triple Alliance.
• France and Britain had already formed a "friendly agreement", the Entente Cordiale, putting to bed literally hundreds of years of rivalry, agreeing to protect each others colonial investments and not compete for territory with each other. Russia joined this a few years later, despite their own ongoing rivalry with Britain in the Middle East and India, forming the Triple Entente. This wasn't quite a military alliance, more an agreement to cooperate politically in opposition to the Triple Alliance.
• The wildcard was the Ottoman Empire, based out of modern day Turkey and controlling much of the Middle East. They were in contention with Britain and Russia for control over the Middle East, and with Britain and France for Egypy and North Africa. They weren't part of any formal alliance, but were willing to join any war against Britain and Russia.

So how did the war actually start?

In 1917 a Serbian nationalist assassinated the heir to the Austro-Hungarian throne while he was visiting Bosnia, which led Austria-Hungary to demand Serbian submission which they refused, so Austria-Hungary invaded. Russia came to their defence, Germany joined Austria-Hungary in the war against Russia, while Italy stayed out of it because the Triple Alliance was technically a defensive pact and they viewed this as a war Austria-Hungary had started.

France started mobilising to join Russia, so Germany declared war on them too to try and get the jump on them. Rather than invade directly through the heavily defended border, Germany invaded through Belgium and Luxembourg trying to seize Paris and force a quick French surrender. Britain had so far held off on joining either side of the war and might have continued to stay out of it; remember, the Entente Cordiale wasn't technically a military alliance. However, Britain had guaranteed Belgium's independence from France or Germany since the 1830s so, when Germany invade Belgium, Britain declared war on Germany.

The Germans failed to quickly take Paris, being halted by the British and the French at the First Battle of the Marne. Both sides dug in and tried to outflank each other, starting the "race to the sea" and the trench warfare the war is most famous for. The Ottomans joined the war on the side of Germany and Austria-Hungary, the Central Powers, and fighting continued for 4 years.

The War ended in the Armistice on 11th November 1918, with the abdication of Kaiser Wilhelm II and the loss of much German territory and influence through the Treaty of Versailles. This Treaty was seen as incredibly harsh and unfair by the German people; France wanted to basically crush any hopes of Germany ever again becoming a superpower; and this fueled the rise of Hitler's brand of German Fascism that fueled WWII.

It's considered the first "World War" because of the involvement of people from around the world who got dragged into what was essentially a European power struggle between their colonial overlords. It wasn't by any means their war, there was no ideological stake in joining like there was in WWII, but they fought and died in it anyway.