A reciprocal pronoun is a type of pronoun that shows that two or more people or objects are carrying out an action and receiving the consequences of an action at the same time. In English, there are two main reciprocal pronouns: "each other" and "one another." They are somewhat related to reflexive pronouns, in that the subject doing the action is also receiving the verb's action. A reflexive pronoun generally indicates one action, however, whereas a reciprocal pronoun indicates the subjects are doing separate, but related, actions, and always has a plural subject.
A very common reciprocal pronoun phrase is "each other." This phrase would indicate the subject of the sentence is two people or things, and also suggests they each performed different, but similar, actions. For example, take the sentence: "Bob and Mary gave gifts to each other." The two individuals comprising the subject of the sentence are each performing the action with separate direct objects, meaning they are not giving the same exact gift to each other. Instead, they are giving different gifts in different actions that are very similar and happening simultaneously.
The other reciprocal pronoun phrase is "one another." Much like each other, one another refers to a plural subject, but instead of indicating the subject is just two people or objects, this indicates more than two. For example, take the sentence: The students talk to one another. In that example, the indication is there are more than two students, although the sentence does not provide information as to the exact number. Further, the action of the sentence, talking, is being done and received by all the students in the group.
Just as with nouns, it is possible for an reciprocal pronoun to take a possessive. For example, take the sentence: "The sisters shared each other's clothes." In this case, the sisters are both doing an action, sharing, and the possessive shows ownership of the clothes. In this case, the clothes belonged to both of them. The same construction can also be used with the phrase "one another."
Technically, the phrase "each other" could also be used to indicate more than two. There is no concrete grammatical rule regarding this usage. For the purposes of being absolutely clear, however, the preferred phrase for more than two is "one another." While it may not be technically incorrect, the slight variation between the phrases could give readers a contextual clue that can help clarify meaning. By contrast, the phrase "one another" should never be used when referring to just two people or objects.