Have you ever played with building bricks? You know how you can use different shapes and sizes of blocks to build different things? Well, in math, we can also use different "blocks" to build things, but instead of bricks, we use "structures".
A quasivariety is like a special set of structures that all have something in common, like a family of structures that all follow the same rules. These rules might include how the structures are built, how they can be combined, or what kinds of similarities they have.
It's like having a group of friends who all love the same things and follow the same rules. They might all have different hobbies and interests, but they all have a common bond.
In math, quasivarieties are useful for studying these commonalities and exploring how the different structures in the family are related. We can also use them to create new structures by combining the "blocks" in different ways.
So, just like you use your building bricks to create new things, mathematicians use quasivarieties to create and study new structures.