Gringo

“Gringo” is a term used for when an American goes to Mexico. There’s a myth that the term comes from the Mexican-American War in the 1840s, when soldiers were singing “Green grow the lilacs, o!” (with “green grow” mis-heard as “gringo”). Gringo probably means “Greek,” as in “it’s all Greek to me.”
 
 
Word Origins
Gringo is a borrowing from Spanish and is alteration of Griego, or Greek. In Spanish, the phrase hablar en griego, to talk in Greek, means to speak unintelligibly. This is akin the English phrase, it’s Greek to me. Both apparently come from the Medieval Latin proverb, graecum est; non potest legi, it is Greek; it cannot be read.

P. Estaban de Terreros y Pando’s 1787 Diccionario Castellano contains the following:
 
Gringos, Ilaman en Malaga a los estranjeros, que tienen cierta especie de acento, que los priva de una locución fácil y natural Castellana; y en Madrid dan el mismo, y por la misma causa con partiuclaridad a los Irlandeses.”
(Gringos, they call in Malaga those foreigners who have a certain type of accent which keeps them from speaking Castilian easily and naturally; and in Madrid they are given the same name, and for the same reason, particularly to the Irish.)

So a gringo is a foreigner, a stranger.
 
The transfer to English occurred during the 1846-48 Mexican-American War. It’s English usage is first recorded in J.W. Audubon’s Western Journal of 1849:

“We were hooted and shouted at as we passed through, and called ‘Gringoes.’”
 
There is a popular, but incorrect, story that the Yankee soldiers of the Mexican war were fond of singing a song, based on a Robert Burns poem, which was popular at the time, the refrain of which went, “Green grow the rushes, O.” (Alternative versions of the tale give it as “Green grow the lilacs.”)

According to the tale, the Mexicans, probably as tired of hearing the song as you are of the latest Top-40 hit, began calling the Americans green grows, which eventually became gringos. Although the tale is associated with the Mexican war, the story is disproven by the earlier Spanish uses of the word.
     
Wikipedia: Gringo
False etymologies
A recurring false etymology for the derivation of gringo states that it originated during the Mexican-American War of 1846-48. It has been claimed that Gringo comes from “green coat” and was used in reference to the American soldiers and the green color of their uniforms. Yet another story, from Mexico, holds that Mexicans with knowledge of the English language used to write “greens go home” on street walls referring to the color of the uniforms of the invading army; subsequently, it became a common habitual action for the rest of the population to yell “green go” whenever U.S. soldiers passed by. This is an example of an invented explanation, because gringo was used in Spanish long before the war and during the Mexican-American War. Additionally, the U.S. Army did not use green uniforms at the time, but blue ones.

Another legend maintains that one of two songs – either “Green Grow the Lilacs” or “Green Grow the Rushes, O” – was popular at the time and that Mexicans heard the invading U.S. troops singing “Green grow…” and contracted this into gringo.

Other uses
In the context of Mexican cuisine, a gringa is a flour tortilla taco of spiced pork (carne al pastor) with cheese (mostly Manchego, Chihuahua or oaxaca cheese). The combination is heated on the comal until piping hot and then served with a choice of salsa. The flour tortilla is white, with brown spots, similar to white skin with freckles.

In the 1950s in Mexico, the 50 pesos bill was called “ojo de gringa” (“Gringa’s eye”) because it was blue.
 
(Oxford English Dictionary)
Gringo
[Mexican Sp.]  Among Spanish Americans, a contemptuous name for an Englishman or an Anglo-American. Also attrib.
1849 J. W. AUDUBON Western Jrnl. (1906) 13 June 100 We were hooted and shouted at as we passed through, and called ‘Gringoes’. 1871 Republican Rev. (Albuquerque, N.M.) 14 Jan. 2/2 Three Mexicans from Socorro..calling her a gringo bitch, finally threw her on the body of her husband.
   
August 1839, Southern Literary Messenger, “A Journey Across the Andes” by W. B. H., pg. 514:
My colleague had previously arranged that this challenge should be answered by the officer of our boat, whose Gringo accent would prove that he was not a Chilian.