Meaning of "Never get involved in a land war in Asia" in The Princess Bride?

"Never fight a land war in Asia" is one of those weird aphorisms that is widely known, but on which nobody agrees who originally said it. It has variously been attributed to Bernard Montgomery (British General), Dwight Eisenhower (American General and later President), and Douglas MacArthur (American General).

The line was in the original book by William Goldman which was published in 1973. At the time, the US was trying to extricate itself from the Vietnam War. Many Americans thought the war a terrible mistake, and "Never fight a land war in Asia" was a frequently heard "obvious truth". A significant fraction of the viewers of the 1987 film would have clear memories of that period of American history.

As @ToddWilcox notes in a comment, the line worked as humor (at least back then) because it brazenly breaks the fourth wall and inserts a highly topical meme from the "real world" into a fairy story where it makes no sense: there is no indication of Asia even existing in the world of The Princess Bride.

As the origins of the quote lapse into obscurity, the humor of it may begin to fail.

Getting involved in a land war in Asia is a classic blunder in the real world. Examples from before The Princess Bride include:

• The Korean War
• The Vietnam War
• The Russian War in Afghanistan

All three were land wars in Asia that have been seen as mistakes. Grave mistakes. Epic blunders. Arguably the most famous classic blunders.

You could also include multiple failed attempts to invade Russia from Europe, the most famous of those being Napoleon’s march into Russia that basically destroyed his once powerful army. Very famous blunder.

The other answers are correct about the general reference - there are numerous examples in real Earth history of disastrous land wars in Asia. But what the other answers seem to miss is that The Princess Bride seems to take place on what we might call "mostly Earth."

There are certainly references to things that seem not to exist on Earth: the countries of Florin and Gilder, shrieking eels, R.O.U.S.es, The Cliffs of Insanity. But there are many more examples of things that do resemble our own history and environment.

Of course, the presence of humans, horses, pigs, hippos, peanuts, and suchlike already suggest that we're on Earth. Probably even more compelling are these quotes from the film:

DO YOU WANT ME TO SEND YOU BACK TO WHERE YOU WERE, UNEMPLOYED, IN GREENLAND!!!

I could give you my word as a Spaniard....

Inigo Montoya: You are using Bonetti’s Defense against me, ah?
Man in Black: I thought it fitting considering the rocky terrain.
Inigo: Naturally, you must suspect me to attack with Capa Ferro?
Man in Black: Naturally, but I find that Thibault cancels out Capa Ferro.
Don’t you? Inigo: Unless the enemy has studied his Agrippa… which I have.

These are references to real-world Italian fencers, Rocco Bonetti, Ridolfo Capo Ferro and Camillo Agrippa, and the Dutch fencer Gérard (Girard) Thibault d’Anvers.

Let me put it this way: have you ever heard of Plato, Aristotle, Socrates?

Because iocane comes from Australia, as everyone knows, and Australia is entirely peopled with criminals

The real Roberts has been retired fifteen years and living like a king in Patagonia.

Now, the fact that we're on "mostly Earth," rather than Earth, suggests that the land wars in Asia needn't necessarily represent anything that happened in our real history. However, considering that Vizzini appears to know about the transport of British and Irish prisoners to Australia, which occurred between 1788 and 1868, it seems reasonable to suppose that The Princess Bride takes place sometime after Napoleon's invasion of Russia in 1812.

A counter argument could be made that the costumes and technology we see do not at all resemble 19th century Europe. However, this is very common even in films which are supposed to take place on actual Earth. Consider Braveheart and William Wallace's

farcical representation as a wild and hairy highlander painted with woad (1,000 years too late) running amok in a tartan kilt (500 years too early).

Freedom's Sword

Vizzini is an idiot, but he is not uneducated. He has book knowledge, but not intelligence or wit, nor does he read context very well. That one quote paints this picture perfectly.

For him to know to never get involved in a land war in Asia requires him to have studied military history. This is not something an uneducated man would know.

But for him to think that this is the most important nugget of knowledge shows how out of touch he is with himself. He is not in any position to command an army, let alone in Asia. This knowledge will never benefit him. He is contextually oblivious to himself.

And this is the best case scenario for him. If he was merely regurgitating knowledge he did not study himself, or if he mentioned it just to boast about knowing such an esoteric nugget of wisdom, only paints him as an even bigger idiot and/or contextually oblivious fool.