I wrote a small paper on the Belgian military during WWI when I was studying in France last year. I don't have the paper anymore, so I can't give you the sources I used, but I'll write down what I can remember. During the German invasion of Belgium, the Belgian army put up a fierce resistance, despite being outnumbered, outgunned and the fact that the German military was better trained. The Germans had expected to simply march through Belgium, but were instead met by heavy resistance at places like Liège and Antwerp, cities that had impressive fortifications built around them. This bought some time for the French and British armies. This caused the German army to commit quite some atrocities against the Belgian population, like the sack of Louvain (Leuven).
That's where the term 'Brave little Belgium' comes from, by the way. It was a small neutral country invaded by the largest military force of the time. Despite that, it resisted far longer than expected and it paid a terrible price for it. A mighty propaganda tool for the Allies. Anyway, eventually the Belgian army dug in around Ypres, where it held with its British allies for the remainder of the war. The Belgians did no offensives in this time: it was apparent to the Belgian king Albert I and his general staff that the offensives of the Allies cost them a lot of troops for minimal gains. Belgium didn't have a lot of troops to spare (if I remember correctly, by the end of the war they had some 260 000 troops). However, because they did gather more recruits as the war dragged on (expats from France and Great Britain, some of whom had crossed the Dutch border, taken a ship to the UK, joined the Belgian army there, were then shipped to Le Havre in France and from there went back to the Belgian front), they agreed to take over larger sections of the trenches to relieve the British army which would then have more offensive power on the by then smaller sections that it controlled itself.
The Belgian army did go on the offensive towards the end of the war, to liberate occupied Belgium. Another reason for this was that Albert I was more concerned with Belgian sovereignty than with the Allied war goals. He remains one of the most popular Belgian kings.

There was a detailed post on the role of Belgium in WWI that you might find interesting. The short version is that the Belgians wrecked the invasion schedule by destroying their own bridges and placing barricades, which may have prevented a repeat of 1870.

Besides the European war, Belgium also had a colony in Africa, the Belgian Congo. There, Belgian troops (composed of some whites (usually serving as officers), but mostly local blacks) invaded the German colonies and especially in German East Africa succeeded in capturing some territory, including the city of Tabora.

It's a good question because 'brave little Belgium' refers to the Belgians' diligence and resistance movements but no one ever talks about what military purpose they had.

The Belgians made indirect contributions, by smuggling lettres and food and they brought other people to Holland so they could go to England to join the army. They also made direct contributions, the most important of them being the Battle of the Yser. The Germans never crossed the river Yser because of the Belgians.

The problem with Belgium is that they had a new general staff and they were a little incompetent. It's counterfactual, but maybe Belgium could've done more when the general staff was able to take care of it?

Source: I'm Belgian/French and a history student. Everything I wrote is basic knowledge for me. If you want to know more, you can read The War of 1914 Military Operations of Belgium in Defence of the Country and to Uphold Her Neutrality