Neural networks
An activation function is the small rule inside each neuron that decides how strongly it fires, and it lets neural networks learn curved, complex patterns.
After a neuron adds up its weighted inputs, it applies an activation function to that total. The function might say 'if the total is negative, output zero; otherwise pass it through.' That particular rule is called ReLU and is the most common one. Others squash the number into a range between zero and one.
Why bother? Without activation functions, stacking layers would be pointless: many layers of plain addition and multiplication collapse into one simple line. The activation adds a bend. With bends at every neuron, the network can trace any shape, which is what lets it model messy real-world patterns.
The choice of activation affects how easily a network trains. Some older ones caused signals to fade away in deep networks, which held the field back for years. Simple ones like ReLU fixed that and helped make deep learning practical.
A dimmer switch that stays fully off until you turn it past a certain point, then brightens smoothly, behaves like the most common activation function.