Each self refers to each person or individual.
This is a jukugo word, which usually means on'yomi readings from the kanji. If you know the readings of your kanji you'll know how to read this as well.
You need to bring your own bento box for the school trip.
When I entered the Tofugu office, each worker was lying in a comfortable position.
The only thing we can do at this point is let each person decide on their own.