The phrase Mexican Standoff is a confrontation where there are no winners or losers.
All parties (usually pictured as 3, but the same can be achieved by only 2 parties) are in a position if they were to do anything, it would lead to their own demise.
There is no way to resolve such a standoff without an outside event, that would change the circumstances.
The USA and the Soviet Union was in a very similar standoff during the “cold war”.
The term Mexican Standoff came from the 19th century Mexican American war or from the many confrontations by Mexican bandits.
The exact origin is unknown, but it was first used in Mexico, hence the term is called Mexican Standoff.
The term Mexican Standoff is rarely used nowadays, hoever back in the early days of television, it was a popular thing, like in movies starring Clint Eastwood.
It can only be seen in movies, TV series and some parody videos on video sharing website like YouTube.
Usually it is used by comedians to give their crowd a good laugh, like the famous comedian duo Key and Peele, who used the term for a skit in a 2013 in a YouTube video.