Goodyear welt shoe construction utilizes a piece of material, the welt, which is stitched to both the insole and the upper of the shoe, and creates a point where the sole can be attached. The empty space that is enclosed by the welt is filled with cork or other porous materials for breatheability. The sole is then both stitched and glued to the welt.
The beauty of the goodyear welt construction is that it is almost waterproof as a result of the way various parts of the shoe are attached to the welt, the insole is virtually sealed off. The sole can also be removed easily which makes shoes of this construction very popular because they can be made to last many many years if the uppers are kept in good shape. The overall process of the goodyear welt is much longer than other shoe construction methods and results in a more costly shoe, but goodyear welted shoes are extremely popular due to their substantial benefits.
In 1869 Charles Goodyear Jr., the son of Charles Goodyear the namesake of Goodyear Tire Co., invented the machine which allowed the goodyear welt process to occur. The construction method is obviously named after him.
(sources: chestofbooks.com, en.wikipedia.org)