If you are playing games on an XBox 360, it is very important that you understand how profiles and save games work. They are tied together very closely!
First, a profile is an account that a gamer log into to play games. Any time that gamer then hits SAVE in a game, the save game is created that is tied to that profile. So if you make a profile named
and then you sign in as Lisa, every game file you save will be associated with the name Lisa. All the achievements you unlock will belong to Lisa.
Why does this matter?
Let's say you go over to a friend's house and bring along your Lisa save game on a memory card. You probably won't be able to play it! That is because only Lisa can access that game.
With *some* (not all) games, you can move the game save file to belong to a new username. So Bob can move the game save file to belong to the Bob username. Once that happens, though, no more achievements can be unlocked.
This is for very legitimate reasons. Let's say Lisa gets 99% of the way to the end of a game, and then saves the game. Now Lisa hits 100% and gets the full game achievement. She gives the game to Bob, and Bob plays for 5 minutes and gets the achievement too. That wouldn't be fair!
However, what if Lisa wants to go play her save game at her grandparent's house while she is visiting? What she does is move the save game AND the profile onto the memory card. Now she can use her profile - which is valid - and the save game that matches that profile - on the machine at her grandmother's house. The two go together and work as a pair.
How about if this gamer tag is an XBox Live enabled gamertag? What you have to do here is a little more dangerous. You move the profile and save game - and when you go online at the new location, it DEACTIVATES the old one (i.e. your home system). It does this to prevent theft, so that you don't end up with 100 "Lisa" people around the world all going onto XBox Live with the same gamer tag. Once you get home again, you activate the tag on your home machine and it automatically deactivates at grandma's house.
Why this is dangerous is it depends on XBox Live working smoothly. I have heard from MANY people that when the XBox Live servers are busy, that the recovery process fails. It can take them multiple days of multiple tries. If you're in this situation, make sure you try at all times of the day or night, because it could be the server you're on is most available at certain times of the day.