The Weld Boundaries tool exists to support a particular workflow for advanced mesh repair. Many of these repairs can now be handled by the Bridge tool, which did not exist at the time Weld Boundaries was added. However, this workflow is still useful and so we will describe it here.
The Weld Boundaries tool requires two disjoint input selections, each of which contain boundary edges, and some of these boundary edges should be coincident in each selection. In short, the selection should be two sides of a "crack" in the mesh. After running the tool, the two sides of the crack are welded together (hence the name). The crack must be shaped such that there is a one-to-one correspondence between crack vertices / edges.
This may seem like a very special case, however if you have long, thin holes in a mesh, you can use one of our sculpting brushes to "pull" the sides of the hole together. The brush to use is the ZipperEdge brush in the Volume Brush tool (circled in red in the image to the right). Scrubbing with this brush along a hole boundary will cause the two sides of the hole to pull together, assuming the brush is sized large enough that the two sides lie within the brush volume.
The main benefit of this workflow is that the ZipperEdge brushing will "auto-magically" clean up very low-quality mesh boundaries. The combination of remeshing and smoothing resolves many issues that would cause poor results with either the Join tool, or the Bridge/Fill workflow. This Zipper/Weld approach can also be used as a way to combine different meshes into a single object.
The image below shows an example of this workflow, that you can easily try yourself on the Bunny model. On the left is a large hole that could not be filled directly. Second-from-left, we use the ZipperEdge brush to pull the two sides together. Then we select on each side of this crack, and use Weld Boundaries to remove the crack in the rightmost image.