I just received a gift card through mail and it says the code is invalid when I try to redeem it?

What sort of gift card (if it's an Apple Store gift card then you won't be able to redeem it onto your iTunes account, they are for use with the online store and bricks-and-mortar stores), and the card was issued in the country that you are in and which you therefore on your address on your account (all iTunes gift cards are country-specific) ?

If it is an iTunes card for your country and it's being accepted then try contacting iTunes Support (if you got the card from Facebook then contact Facebook support) : http://www.apple.com/support/itunes/contact/ - click on Contact iTunes Store Support on the right-hand side of the page, then iTunes Cards And Codes