Have you ever seen a blacksmith make a horseshoe? Well, no, probably not, but they use a special furnace which is called a forge, and "to forge something" is also the act of bashing that hot object into shape.
Forge has also taken on the more general sense of creating something. A new philosophy or art form might have been forged, as might an alibi or an excuse. To forge something also has the meaning of faking something, such as a painting or a signature with the intent to deceive. It can also mean to move ahead in a steady manner, either physically or metaphorically, much like those solid, regular blows of the blacksmith's hammer.