Blake construction is the bread and butter of the Italian shoe industry. Although Italian shoe manufacturers use a dizzying array of construction techniques, probably more good-quality shoes are made using Blake construction than all of the other methods combined.
The diagram above (again lifted from the La Botte Chantilly website) shows what is involved with Blake construction, and it should be immediately clear why it is so popular: it's a lot simpler than Goodyear welting. There is a single row of stitching that attaches the insole to the upper (turned under the insole) and the outsole. Obviously, since the stitching runs inside of the shoe, it's not possible for a Blake-constructed shoe to be stitched together by hand; so this construction technique is a child of the Industrial Revolution. It's named for Lyman Reed Blake, and American inventor who patented the machine to accomplish this in 1856. He later sold the patent to a man named Gordon McKay, and one consequently sees this construction method referred to as McKay construction.
Blake construction has two principal advantages. First, because it requires no stitching on the sole edges outside the shoe, it is possible to get extremely close-cut soles with it, much more closely cut than would ever be possible with a Goodyear-welted shoe. Second, because Blake-constructed shoes have fewer layers in the sole, they tend to be more flexible than Goodyear -welted shoes. The principal disadvantages are all outgrowths of the stitching along the insole. This row of stitching can irritate some feet, especially when it is not covered by a sock liner. More seriously, it can wick moisture from the ground into the inside of the shoe. Unless they have rubber soles, Blake-constructed shoes will always be less waterproof than Goodyear-welted shoes, all other things being equal.
Shoe snobs tend to disparage Blake-constructed shoes, and I think that this tendency is unfortunate. It is true that Italy turns out a lot of cheap, junky Blake-constructed shoes, but I would put a Blake-constructed shoe from an excellent maker like Gravati up against any comparably-priced footwear, regardless of construction. They're better-made and better-finished than any of the English-made Goodyear-welted shoes that I have seen at a similar price point. And, despite what you might hear from salesmen pushing Allen-Edmonds or other Goodyear-welted shoes, Blake shoes can be resoled. The cobbler just needs a Blake soling machine, which are admittedly less common than Goodyear welting machines, at least in the United States.