When you have an electric charge, it can push or pull on other charges around it. The method of images is a way of figuring out what happens when charges are near something like a wall, or the surface of a conductor.
Imagine that the wall is like a mirror and the electric charge is standing in front of it. The charge will create an invisible "reflection" of itself on the other side of the wall that has the same amount of charge but with the opposite sign. This reflection of the charge is called an image charge.
When you use the method of images, you can figure out what the electric field is like near the wall. To do this, you have to add up the electric fields of the real charge and the image charge. Together, they give you an idea of where the electric field lines are and how strong it is near the wall.