Broadsword may refer to either one of two classes of weapons: a type of sword that possesses double edged blade and a basket hilt or shell guard, or it may also refer generically to multiple types of swords.
Applications in Combat
Broadswords were heavier and broader in the blade than the generic arming sword and was designed almost exclusively for slashing, to hack through armor and bone, as opposed to thrusting. Depending on the make of the sword, it could have a simple straight cross guard and a hilt for a single hand or a single handed sword with a basket hilt that can be used to parry an opponent's blade. A sword with an elongated hilt for two hands and a longer blade technically aren't broadswords, but are used for a similar purpose and allows for more strength in the user's blows, but forces the wielder to use the sword for both offense and defense because the sword's size makes it so a shield cannot be used.
Role in Eragon
Prior to the infiltration of the castle in Teirm, Brom told Jeod that his rapier would be useless against broadswords and flamberges, however Jeod told him not to be ridiculous and that none of the guards had a flamberge and the rapier was faster than a broadsword.
Real World Connections
Under the strictest definition, the term broadsword is applied to heavy swords constructed with a straight blade that is double edged, containing no false edges, whose purpose was cutting and contained a shell guard or a basket hilt.
In recent centuries the definition has become more fluid and has expanded to include other weapons that were not originally included in the class to the extent that the term now serves a generic term that is applied to many different swords.