What does "The fastest xxx in the west" mean?

Solution 1:

There have been many movies made about gunfighting in the American "Old West," roughly the period between the Civil War and World War I when the US underwent a great westward expansion as settlers in the east and south went looking for opportunity. These movies were incredibly prominent in the earlier half of the 20th century, often shown as "serials," or movies that had a different story set around the same character from week to week. In almost all of these movies the hero wins the girl / saves the town / saves himself via a climactic gunfight. This gunfight occurs against a gunfighter who is billed as "The Fastest Gun in the West." The hero, in winning this climactic gunfight, is now the newest "Fastest Gun in the West." This idiom is so powerful it even influences movies that are not about the Old West, including movies like Star Wars.

All of the phrases are a play on this idea. The idea is that our product (or technology or service) is greater than, better than, faster than all of the others. And will help you save the day besides.