She gave each of them two.

Literal

[topic-は] each-person 2-counter [distributive-ずつ] gave.

めいめい ('each, individually') and ずつ ('apiece, each') stack here for emphatic distribution: 'each person, two each.' ずつ attaches to a quantity to mark equal distribution — 一人一個ずつ ('one each per person'), 三人ずつ ('in groups of three'). めいめい on its own already carries the 'each individually' sense, so the pairing is partly redundant for warmth — natural but not strictly necessary. やった is the past of やる ('do, give'), here in the 'give' sense (やる can mean 'give to a peer or inferior' — to a superior the verb shifts to 差し上げる).