They gave each other gifts for Christmas.
RECIPROCAL PRONOUNS
Reciprocal pronouns are pronouns which are used to indicate that two or more people are carrying out or have carried out an action of some type, with both receiving the benefits or consequences of that action simultaneously. Traditionally, each other refers to two people and one another refers to more two people, but this distinction is disappearing in modern English.
We also use possessive forms, each other’s and one another’s.