From a grammatical perspective, ‘each other’ and ‘one another’ essentially have the same meaning – they are used to show that each member of a group does something for/to the other. For example, the sentence, ‘Jim and Janet like each other’ implies that Jim likes Janet and Janet likes Jim.

Each other is more common than one another: Rick and Gina never liked each other. (Rick never liked Gina and Gina never liked Rick.) Everyone in the family gave each other presents. (Each member of the family gave each member of the family a present.) How’s Maria? Do you see her often? She’s great.