It is the process of repairing a torn garment thread by thread. Generally tears are mended by sewing or patching, but on occasion there will be a special garment that is torn in a place or in a way that a visible sew or patch will just not do. Instead, you need a weave. Weaving is labor intensive, and is expensive.
It doesn’t return a garment to “new” condition in all circumstances, & may still result in a visible repair, though the repair will be of much higher quality than can be obtained by any other means.
These photos provide perspective on the before/after results of a weave
The thread on the right photo is just there to provide visual center to the weaved patch. If you look closely at the photo on the right, you can see the outline of a patch that has been expertly weaved into the fabric of the sleeve.