This is the 4163rd most frequent Russian word.
свое
"One's own" or "of one's own."
In this sentence, "свое" is used to indicate possession, meaning something that belongs to the subject of the sentence ("each of us").
Каждый из нас должен заботиться о своем здоровье.
Each of us must take care of our own health.
Here, "свое" specifies that the homework belongs to the person being referred to and varies with context based on the subject.
Учитель попросил принести каждый свое домашнее задание.
The teacher asked each to bring their own homework.
In this example, "свое" shows that the favorite spot belongs to "her" and is used to emphasize the possessive relationship aligning with the subject.