Erwidern is quite formal (it is hardly ever used in spoken language outside of legal or political discussions, more commonly encountered in written form). It means to reply to a question or a statement. An alternative that shares the same basic meaning would be entgegnen, which I would also consider rather formal. Antworten is certainly the most common way to express that someone is responding to a question.
In addition, erwidern is also used to more generally express that someone is retaliating or reciprocates someones actions, e.g:
Die Soldaten hatten den Befehl, im Falle eines Angriffes das Feuer zu erwidern.
They were to retaliate in case of an attack, but not allowed to fire first.
Sie erwiderte seinen Blick.
They exchanged a glance (some kind of mutual understanding is implied here).
Er erwiderte ihre Gefühle.
He returned her affection/had the same feelings for her.