Okay kiddo, imagine you have two types of toys - let's say toy cars. One is made by Company X and the other is made by Company Y. Now, they are the same toy car, but they each have a different design and they can't work together.
This is kind of like what happened in the old days with technology. There were different types of ways to store information, like music or movies or pictures, and each way was called a format.
Now, different companies made different formats that were used to store things like music or movies or pictures. For example, Company X might make a format called "SuperPlay" and Company Y might make a format called "MegaMovie". People would go to the store and buy their preferred format and use it to store or play their stuff.
But what happened, sometimes, is that two companies would make very similar or equivalent formats. And they wouldn't be able to work together. This caused a conflict called a "format war" - because different people would buy different formats, and they would fight over which format was better.
The format war could last a long time, with each company trying to convince everyone that their format was the best to use. People who chose the losing format would be stuck with a bunch of things that they couldn't play or use because their format was no longer being supported.
Thankfully, these days we have moved past format wars since most formats now work with each other, which means we can easily store and play all sorts of things no matter what format they are in. Pretty cool, right?