Immunodiffusion
First let's start out with a chemical analog of immunodiffusion. You know that when you mix solutions of silver nitrate (AgNO3) and sodium chloride (NaCl) together you obtain a copious amount of white precipitate. While the soluble ions of nitrate and sodium do not interact, those of silver and chloride do - silver chloride is quite insoluble.
Now let's do the reaction more slowly: allow the silver and chloride ions to diffuse toward each other through a gel such as a starch gel. The silver nitrate is put in a small well at one end of the gel and the NaCl in a well at the other end. The ions begin diffusing out of their wells. Eventually the silver ions and the chloride ions meet, link up and precipitate making a white line in the gel.
Antibodies and their target antigens do the same thing. When they meet, they form are precipitate: a lattice of interconnected antibodies and antigen molecules. This lattice in immunology parlance is "precipitin."
Precipitin only forms when the antibody latches onto the antigen molecules. This is highly specific.
Sometimes the immunodiffusion plates (often named after their inventor Prof. Ouchterlony), show more than one precipitin band between the antibody and antigen wells. This is because large antigen molecules are so big that different parts elicit different antibodies to be made. Thus the antibody preparation actually might consist of more than one type of antibody - each type will interact with its own target portion of the antigen molecule.
Sometimes you might have two closely related antigen molecules. Most of their regions are identical, but one is not. Antibodies made against one of the antigens, will react with the identical portions of the other antigen, but not with the non-identical part. Thus while there might be three precipitin lines with the original antigen, there might only be one or two lines with the related antigen. Those lines are from what is called "cross reaction."
Cross-reaction precipitin lines from sharp corners when the two related antigen wells are arrayed around the antibody well.