This is the 5497th most frequent Japanese word.
えみ
"えみ" (emi) means "smile" or "grin" in English.
Here, 'えみ' (Emi) is used as a proper name of a person, indicating the subject of the action in the sentence.
えみは笑顔で話しかけてきました。
Emi approached me with a smile.
In this sentence, 'えみ' refers to the smile of a baby, used as a noun indicating a facial expression.
赤ちゃんのえみを見ると幸せな気持ちになります。
When I see a baby's smile, I feel happy.
Here, 'えみ' represents the action of smiling, used metaphorically to describe the emotion surfacing as a smile.