The western front was fought in France and Belgium mainly. The nations fighting there were Britain, France and Belgium (with their allies, such as colonies and places like Portugal and Newfoundland) against Germany and some of its allies. Battles such as Verdun, the Somme and Cony ridge were fought on the western front. Warfare here was predominately fought in trenches, and was very slow moving, with little land being gained at a time. Meanwhile, the eastern front was were Austria Hungary did a lot of fighting. Here, Austria Hungary and some of its allies such as Bulgaria fought Russia and smaller countries like Romania. Some of the battles fought here were Tannenburg, Masurian lakes and Bolimov. Here, land was gained and lost much faster.
The difference comes because the eastern front was in Eastern Europe, while the Western front was, of course, in Western Europe. There were other theaters in the first world war too, such as in the Middle East, the Mediterranean and the Alps. So to conclude, the western front was named so because it was in western Europe, and the eastern front in eastern Europe. Hope this helps!

A 'front' refers to the area of military operations - it may be a contraction of 'front-line'. In 20th-century warfare, where massive numbers of soldiers, long-ranged communications, and technologically-advanced weapons allowed and forced armies to fight effectively across hundreds of miles rather than in relatively compact concentrations, the 'front' came to refer to lines drawn across massive areas.

The Western Front, therefore, was the area of operations occupied by the German, French, British, Belgian, and (later) United States armies in Western Europe, from the Alps to the Flemish coast. Fighting here was characterised by the presence of trench warfare, massed artillery bombardments, and relatively small breakthroughs rather than a war of manoeuvre.

The Eastern Front is less well-defined, because it was a less constant front; fighting here often still was a war of manoeuvre. German, Russia, and Austria-Hungary operated here, as did countries like Romania, and Serbia.

However, the 'Eastern Front-Western Front' model doesn't take into account the whole war; there was a front between Italy and Austria-Hungary in the Alps and the Venetian coast for much of the war, with fighting in the alps being especially difficult and vicious. The Balkans saw much fighting; as previously mentioned, Serbia participated in the war, but there was a combined French-Greek attack on the Ottoman Empire in the Balkans, which resulted in the capture of Thessaloniki (called Salonika by the Ottomans). The British Empire fought the Ottoman Empire in the Dardanelles offensive, and rather more successfully through Egypt, the Levant and Mesopotamia. Further, the French, British and German Empires clashed in Africa. Japan also took some German colonies in the Pacific.

In addition, WWI was a naval war; the Royal Navy and the Imperial German Navy clashed at the Falklands before the RN managed to bottle the Kaiserliche Marine up in the Baltic; the KM's attempts to break free resulted in the Battle of Jutland. The Mediterranean saw limited naval fighting, and the Black Sea became a battleground between the Ottoman and Russian navies.

The 'Allies' in WWI is a term used to describe, broadly, the side that Britain and France were on. One term also used is Entente, after the Triple Entente, an alliance between Britain, France, and Russia in the leadup to the war. As Belgium and Serbia found themselves on the Entente side, 'Allies' tends to be used as a slightly more accurate term, especially after Italy, Japan, and the United States joined the war (and Russia, one of the three Entente powers, was knocked out of the war by its revolution). 'Central Powers' refers to Germany and Austria-Hungary. who were in the centre of Europe between the Entente powers. Italy had originally been allied with Germany and Austria-Hungary, but refused to join in 1914 and joined the Allies in 1915. The Ottoman Empire also joined this side due to historical enmities with Russia and fears of further British expansion.