The Germans didn't capture them per se; the British retreated from the position in the night of August 23/24.

At first glance, the Mons position looks strong, but it was ultimately untenable. Although the canal presented a barrier to the German assault, it bent around the town of Mons and jutted forward, creating a salient that was exposed to German enfilading fire.

Initially, the British inflicted heavy casualties. British units entrenched the forward slopes on their side of the canal and had a clear line of sight to the advancing German infantry. British prewar training also emphasized marksmanship more than training in the French or German armies, and British riflemen inflicted heavy losses on the lead elements of Alexander von Kluck's German First Army as it stumbled into the British lines. John Terraine claims the Germans mistook British rifle fire for machine gun fire, but the validity of that claim has been contested recently.

As I noted above, the problem with the position was that it formed a salient and was therefore exposed to German artillery fire on three sides. Moreover, British trenches on forward slopes gave infantry a clear field of fire, but they were horribly vulnerable to German shell fire. For example, the 4/Middlesex Regiment in 3rd Division suffered 400 casualties (roughly 40 percent of its allotted strength) at Mons.

German First Army was simply too strong for the BEF to hold off. It was the biggest of the six German armies on the Western Front (several corps compared only two British corps) and was saturated with heavy guns needed to break through the Belgian fortresses. The British position at Mons was already falling apart when Charles Lanrezac's French Fifth Army withdrew, leaving the BEF's right flank exposed. When word of this reached Sir John French, the commander of the BEF, he ordered his army to fall back, beginning the Great Retreat that ended at the Marne.

Sources: Terraine, Mons (old but remains a good source); see also Gardner, Trial by Fire; the stuff about the forward slopes comes from my own research, Dykstra, "Entrenchment, Field Fortifications, and the Learning Process in the BEF"; for the German perspective, Herwig, The Marne is a good place to start.