This bags is called a morral and is carried like a messenger bag across the body. Morrales are made by men out of wool. I bought this (used) one because I liked that it had a name woven into it. This is either the name of the man who made it or the man for whom it was made (or both!). The front says "Diego Jacinto M." and the back says "DGM".
The strap is hand-woven as well, with an interesting adjustment mechanism. Attached to the bag is a loop, and the strap is tied to the loop at the desired length. The strap ends in two braids.