The shutter strap is the fabric band used to raise and lower a roller shutter by hand. At the top it winds onto the pulley on the axle and at the bottom onto the winder on the wall.
It is the part that works hardest and the first to wear out. It rubs where it comes out of the shutter box and dries out in the sun, so over the years it frays.
When you see loose threads or the strap getting thinner along a stretch, replace it before it snaps, because it usually breaks with the shutter down. In the meantime, do not pull hard if the shutter sticks. It is all explained in shutter repair.