Well, acetylsalicylic acid is somewhat absorbable through the stomach walls, and anything that gets it into the bloodstream faster is what a person with a headache or backache wants, or will at least claim to want during throbbing pain.
That assumes the stomach isn't irritated by the arrival of the aspirin, which is a different response for different people. The capsule may be enteric coated, which will survive the stomach's digestion, until the pill reaches the small intestine.
You can also heavily buffer the pill, so acid doesn't arrive at the wrong moment and irritate the stomach. As I understand it, the sodium bicarb in Alka-Seltzer isn't meant to buffer the aspirin, it's meant to address stomach upset from other sources. But then again, large amounts of antacids can upset the stomach too.