Several reasons, largely related to security and trade. Belgium, and the Low Countries more generally, have historically been known as "the Cockpit of Europe" (as in cockfighting) for the many, many battles that have been fought there. The whole region is agreeably flat and excellent for the movement of armies, either into France from the northeast, or from France towards Germany. The Duke of Marlborough won some of his greatest victories there, the French Revolutionary Wars began there with a French invasion of the Austrian Netherlands, and the Napoleonic Wars ended there with the Battle of Waterloo. In the aftermath of the Napoleonic Wars, the United Kingdom of the Netherlands was created as a buffer against France. The Kingdom of Belgium broke away from the Netherlands in 1830, and in 1839 the Netherlands finally recognised Belgian independence with the Treaty of London. At Britain's insistence, the treaty also guaranteed permanent Belgian neutrality and committed the great powers of Europe to defend that if it was ever violated. This was considered so important that during the Franco-Prussian War of 1870-1, Otto von Bismarck felt compelled to repeatedly assure Britain that there would be no violations of Belgian neutrality.

From 1904, though, and possibly earlier, the German Army began considering a march through Belgium to outflank the line of massive fortresses the French had built on the frontier with Alsace-Lorraine since the Franco-Prussian War. Make no mistake, prior to the start of the First World War both Britain and France were well aware that Germany would make a violation of Belgian neutrality to get round French defences. In fact, the French Plan XVII (and British support) was contingent on Germany violating Belgian neutrality first so they could engage the Germans in Belgium while the bulk of the German Army was fixed in Alsace-Lorraine. What they did not anticipate that the German swing through Belgium in 1914 would come so far west of the Meuse, and in such huge numbers. This actually made things a lot easier for Britain: while one of its motivations to fight was to protect the balance of power in Europe by siding with France, much of the British Cabinet felt that they could not justify war for "a corner of Belgium". It was the sheer scale of the German invasion, and in particular the threat to Antwerp and the Scheldt Estuary, that unified the Cabinet and Parliament behind war in the summer on 1914.

The Scheldt Estuary was and remains the gateway to Europe for Britain's trade (as may be seen on this marvellous shipping map that appeared on /r/dataisbeautiful a couple of days ago). As you can see, shipping from the Scheldt Estuary can reach deep into the continent on those rivers, and it was intolerable to Britain's economic livelihood that another power dominate those ports, especially if, as was feared, the Germans massed the High Seas Fleet there, which would be pointing like a barrel of a gun towards the mouth of the Thames. Add to this the possibility of the Germans occupying the French Channel Ports (as was recommended in Bethmann-Hollweg's Septemberprogramm), and you have the Imperial German Navy threatening Britain's trade with both Europe and the wider world by controlling the passage to the Atlantic.

So, Britain's motivations can largely be summarised as seeking to protect general European security by guaranteeing Belgian neutrality, and then protecting their own security and trade by choosing to defend Belgium, as well as preserving the European balance of power by fighting with France.

Sources:

Max Hastings, Catastrophe: Europe Goes to War, 1914

Hew Strachan, The First World War, Volume I: To Arms

Barbara Tuchman, The Guns of August