The  reciprocal pronoun

The reciprocal pronoun birbiri means "each other ". It brings in the sense of mutual activity to the sentence if the verb is not reciprocal.

birbirimiz  ----> each other of us [one another of us]

birbiriniz  ----> each other of you 

birbiri/birbirleri ---> each other of them

- Durumu anladık, ancak birbirimize birşey söylemedik.

We realised the situation, but we didn´t say anything to each other.

- Birbirinizin kitabını kullanmayın, kendi kitabınızı kullanın.

Do not use each other´s book[s], use your own book[s].

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When it is formed with the third person possessive suffix, it takes an "n" before the case endings ;

- Çocuklar birbirlerine şeker verdiler. 

Some English usage authorities urge the use of each other when referring to two people and one another for more than two people. Yet there’s no logical reason for this guideline, and writers break it nearly as often as they follow it. In practice, the two phrases are interchangeable.We can communucate each other in a daily basis. John, Jane and David going on on vacation in Italy,but only John and Jane can see one another every day while on vacation.Not much of a difference in translation I assume.