A mainframe sort merge is like sorting your toys. Imagine you have a big box of toys that are all mixed up, and you want to put them in the right order. You might first look for all the cars and put them in one pile, then find all the dolls and put them in another pile, and so on. This is called sorting.
Now let's say you have another big box of toys that also need to be sorted. You don't want to mix them up with the first box, so you need a way to put them together without making a mess. This is where the merge part comes in.
When you merge two sets of sorted toys, you take turns picking the next item from each pile and putting them in a new pile in the right order. For example, if you have two piles of cars, one with blue cars and one with red cars, you might pick one blue car and then one red car and so on until all the cars are in order.
A mainframe sort merge works the same way, but with really big sets of data. For example, a bank might have millions of records of transactions that need to be sorted and merged to create a report. The mainframe computer can do this quickly and efficiently, just like you sorting and merging your toys, but on a much larger scale.