The #SPADD constant corresponds to a flag in the sprite attribute bits, which is the last argument to SPDEF or SPSET. By setting this flag, you set the sprite to add blending mode.
What additive blending does is adds the color values of whatever draws under the sprite to the sprite itself. To give an example, if the sprite is red and is drawn over a blue background, it would look purple.
Keep in mind that this model is based on RGB channel colors. Trying to add white to anything or anything to white will just be white again. Adding red to red would just be a brighter red, or the same red. It depends. E.g. if the background is RGB 10,10,10 and the sprite is RGB 5,20,0 then the sprite will be RGB 15,30,10 with add enabled.