while you use a particular weapon, you level it up..when you create a class and choose a weapon on the bottom right of that weaopn picture is the weapon level. when it says weapon level max you can prestige that weapon. click on that weapon and in the middle of that page you'll see a prompt to prestige it..
Advantage is that you gain more xp while using the same gun.....if you max it out, you can restart from square one and get all of the xp points for ranking up your gun again. Also, you keep all of your camos.
Disadvantage is you lose all your attachements. Bit of a pain but I find there are lots of good attachments to use so you can make do.