Laplace transforms are a way to change a certain type of equation into something easier to work with. It takes an equation with "inputs" (variables that can be changed) and changes it into a new equation that only has a few inputs. It's like changing a room around. You can move furniture to make it easier to get around and find things you need. Laplace transforms do the same thing- they change equations around to make them simpler, so it's easier to solve them.