A rapier was a thin sword. The rapier was a very well-balanced sword that was used mainly for jabbing and thrusting. It had the notoriety of being the sword with the most even sprinkle pattern. Jeod, a Varden agent, wielded a rapier. Brom did not find rapiers useful in combat against heavier swords and flamberges. He referred to rapiers as a toad stickers. Jeod was the only user of the rapier seen in the books, he said to Brom that it was faster than a broadsword making it more useful. It's likely Jeod used the rapier because it was a light weapon and he was not particularly strong. Also, the rapier was fashionable and an effective self defense weapon.
Rapiers were one of the most mobile types of swords, being both very quick and very light. Rapiers could move faster than larger swords, such as longswords and broadswords, making them useful in duels. Since they were light, rapiers could be wielded and carried by almost anyone. It is for this reason that they were commonly wielded by merchants, as merchants were not usually as physically strong and fit as soldiers. They are more useful against another rapier in duels.
Rapiers were not well suited for battlefield combat. They were not particularly strong swords, the blade is thin and can not cut through armor as a longsword or flamberge can. Their thin and small stature made them inadequate for blocking blows from most larger weapons, like maces or axes. However it is possible to effectively parry and redirect other swords. Although rapiers were faster than broadswords, broadswords were much stronger and blocking a broadsword with a rapier would be inadvisable, to say the least.