Wiktionary
n. A sack worn over one shoulder with a strap winding around the chest, traditionally used by bicycle messengers.
Wikipedia
A messenger bag (also called a courier bag) is a type of sack, usually made out of some kind of cloth (natural or synthetic), that is worn over one shoulder with a strap that goes across the chest resting the bag on the lower back. While messenger bags are sometimes used by couriers, they are now also an urban fashion icon. Some types of messenger bags are called carryalls. A smaller version is often called a sling bag.
Usage examples of "messenger bag".
Hed brought a messenger bag full of magazines from home and was prepared to wait until I dropped him off at work, or until he was needed, whichever came first.
He grabbed the leather jacket he'd worn last night, and dumped the contents of his messenger bag out on his bed to make room for the flute.
He took the time to take his flute apart and put it back in its case in his messenger bag before following.
A student with an orange messenger bag strapped over her shoulder stops in front of me.