Out of the loop

Let me try getting this to ELI5 levels:

Most programming languages use a way of programming called "procedural programming" (or a variation of that, for example object-oriented programming). A series of instructions gets executed step by step to modify the program's overall state. Imagine it like a cooking recipe. You have control structures like if, while and for that influence the order in which instructions are executed. There are functions (or methods in object-oriented programming) that let you reuse some instructions over and over but that's not quite functional programming.

I'll use a syntax similar to Java, C++ or C# as an example:

void squareAllElements(int[] array)
{
    for(int i = 0; i < array.size(); i++)
    {
        array[i] = array[i] * array[i];
    }
}

Functional programming is a bit more like what you know from maths class. There are still functions that take a list of inputs and produce an output but there is no state to be modified. Every operation must take everything it needs (apart from maybe constants) as parameters and produces new values/objects as an output. You say you know Java, so imagine that none of your methods returns void and every variable can only be assigned once. There are no loops but for example operations that let you separate the first element of a list from the rest or create a new list by applying an operation to all elements of an input. To make that easier, functions can take other functions as parameters.

So let me show the same example in a functional style. This is no specific language, just an example to help you imagine how it works.

int square(int x) => x * x;
int[] squareElements(int[] array) => applyToAllElements(array, square);

Functional programming has its own advantages and disadvantages. It can avoid a lot of bugs because functions can't have unwanted side effects. They just take inputs, return outputs and leave the rest of the world (including their inputs) unmodified. On the other hand, that makes other use cases where you actually want to have some state that changes over time more difficult.

Hope that helps.

Edit: some cleanup and more precise explanations.

Edit: replaced "paradigm" with "way of programming" to make @[email protected] happy.