Okay, so first let's think about what a function is. Imagine you have a magic machine that takes in some numbers and then does something to them, and then gives you a new number as a result. That magic machine is a function!
Now, some functions are easy to understand. For example, you can have a function that takes in the number 2 and then gives you the number 4 as a result (the function is "double the input"). But some functions are more complicated and can't be described as simply.
One type of complicated function is called a "pseudoconvex function". Basically, this means that if you look at the graph of the function, it always looks like it's curving in a certain way. It might look like a bowl or a saddle, but the important thing is that it's always curving the same way.
Now the reason we care about this is because it tells us something about the function itself. If we have a pseudoconvex function, we know that it's always "going in the same direction", which means we can use some cool math tricks to figure out more things about the function.
So in summary: a pseudoconvex function is a kind of fancy function that always curves in the same way, and that gives us some special powers to understand it better.