A gamercard is used to tell other people what you have been doing on xbox live. The pieces of information on a Gamercard include Gamertag, Gamer picture (avatar), Reputation, Gamerscore and recently played games.
Your reputation starts at 5 stars and goes down if you are reported. Most people ignore this.
You get gamerscore from achievments you earn during video games. Each game has 1000 gamerscore. It tells people how much you play.
A Gamertag is your name on Xbox Live. Gamertags are used to be able to search for your friends on xbox live. A gamertag is what random people or people you know will see ex) O Ghillie, XxM4 OGxX . it is pretty much a name you make, keep in mind there are a lot of people on xbox so it will be tough to find the one you like.