s/n = Serial Number. Each product has a unique serial number, it's more of a production number than anything. The higher the number the later in the production run it was. Make sense?
I wouldn't buy a battery for your phone off of Amazon though to be honest, because alot of phones by the same company have very similar looking ones. You might order one with a higher voltage or amperage and damage your phone by using it. You're better off taking it to a specialty store at the mall or something that handles repairs. Typically they have batteries for sale or can order the correct one for you.