Overcasting - can be done by hand - or by machine.
Overcasting is enclosing a raw edge with sewing - so that it doesn't ravel.
If you look carefully, you can see stitches on the edge of one of the pieces - that's done with a serger. It can also be done with a zigzag stitch.
Here is a link to what hand overcasting looks like.
http://www.simplesewingprojects.com/...ercast-stitch/