The Latin Monetary Union was a group of countries, kind of like a club, that decided to use the same money, called the franc, for their countries. The members of the club were France, Italy, Belgium, Switzerland, and later Spain, Portugal, and Greece joined too.
So let's say you went to Italy and needed to buy something, you could use the same money you use in France, like if you went to a different state in the US and you could use your dollars without having to exchange them for a different currency. This made it easier for people who wanted to travel, trade and do business between the countries.
It started in the year 1865 and kept going until around 1927 before it ended, but during this time, it helped make it easier for people in these countries to do stuff without having to worry about different money all the time.