rrumpf said:It does not mean adding them. It more accurately means to "smear" them together, or to "blur" one function with the other. Imagine every point in the first function producing the second function centered at that point, but scaled by the value of the first function at that point. If you do this for every point in the first function, you will have a whole bunch of the second functions overlapping and all scaled differently. The convolution is the sum of all of these.
Does that make sense. A picture and an animation has to exist on the internet somewhere. I would try to google it. To explain convolution, a picture is worth 1000 words and a movie is worth a million words!