Mesh backpacks may seem like a fairly strange invention, but they do have a couple of main uses. What is nice about mesh is that it is transparent. Thus the reason it has become commonly used in schools to prevent students from bringing contraband such as drugs or weapons to school. Scanners are very expensive and it takes a long time to scan all children on a regular basis so see through bags offer a similar level of protection against this problem.
Mesh backpacks are also commonly used in sports to carry equipment. It is nice to be able to see what is in your bag and determine which one you need quickly without having to look inside. Sporting gear tends to need to dry out on occasion so the mesh conveniently allows gear to dry while it is being stored.
Scuba gear is also often kept in mesh backpacks for the same reason as mentioned above. It is nice to be able to store and transport gear in the same bags but when that gear need to dry out properly to avoid damage or mildew mesh is a great alternative.
Aside from mesh backpacks simple mesh bags are also used for similar reasons. Stuff sacs for camping or packing are often mesh. And laundry bags are usually mesh. This serves two purposes. As already mentioned to avoid mildew during storage but also in this case clothes can be washed right in the laundry bag. This may seem odd but if you are in a situation where people are sharing washes and dryers it can come in handy.
Many other bags like military backpacks will also employ mesh as a divider or for extra storage. This reduces the overall weight of the bag and increases functionality.