The Mexican Inquisition was a long time ago, when Spain was a really big powerful country and ruled over a lot of other places, including Mexico. The Inquisition was like a 'court' system that was set up by the Spanish leaders, and they wanted to make sure that everyone in Mexico was following the same religion as them, which was Catholicism. They were afraid that if people followed their own religion, it might make them less loyal to the Spanish rulers or cause problems.
So, the Inquisition would try to find out if anyone was not following Catholicism, and then punish them. This could mean things like putting people in jail, making them do hard work, or even killing them. They would also try to find out if anyone was doing things that they thought were wrong, like magic or witchcraft.
The Inquisition lasted for a long time, and it was a really difficult time for many people in Mexico. Many people were afraid that they might be accused of something, and then punished. But eventually, the Spanish rulers lost control of Mexico, and the Inquisition was stopped. Now, people are free to practice whatever religion they want, and they don't have to worry about the Inquisition anymore.