A heater core is like a small radiator that's inside your car. When the engine heats up, coolant flows through the heater core, warming up the air that passes through it, and that warm air is what blows out of the vents when you turn on the heat in your car.
Think of it like a cup of hot chocolate on a cold day - the heat from the hot chocolate warms your hands, just like the heat from the engine warms up the coolant, and the air passing through the heater core becomes warm so that it can warm up the cold car interior, just like the hot chocolate warms up your insides.
But sometimes the heater core can get clogged or damaged, and that can prevent the warm air from flowing properly. If that happens, it can make your car really cold and uncomfortable inside, especially in the wintertime.