Reciprocal action is when there is mutual action between two parties.

My sisters were talking to each other.

In Greek, there are the following forms:

Singular Plural
Nominative (none) (none)
Genitive (none) ἀλλήλων
Dative (none) ἀλλήλοις/αις
Accusative (none) ἀλλήλους/ας

The reciprocal pronoun is ảλλńλwv “of one another” of each other.  It occurs in the New Testament only in the forms ἀλλήλων “of one another” ἀλλήλοις “to or for one another” and ἀλλήλους “one another.” source

The “to each other” idea is the meaning of reciprocal.  cf. hitpael

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