The Euler Method is a numerical technique used to approximate solutions to ordinary differential equations. It works by taking small steps along the curve of the solution, using the slope at the current point to estimate the next point. This method is particularly useful when an exact solution is difficult or impossible to obtain. To apply the Euler Method, you start with an initial value and a defined step size. By repeatedly calculating the next value based on the previous one and the derivative, you can create a series of points that approximate the solution over a specified interval. This method is named after the mathematician Leonhard Euler.