Why do you need a memory card for this console, what does it do?
Old 3DS uses a SD card while New 3DS uses a MicroSD card. They are used to store games from the eShop, updates, DLC, and media files from screenshot, camera, etc. Instead of buying physical copy of games, you can choose to download them instead.
The advantage to downloading games rather than buying them in a store is:
-You don't need to go to the store, you can get the game right from your house
-You won't lose your game and no one can steal your games. Even if they take the MicroSD/SD card, they can't play the game as it's tied to your account
-All your games are easy to access without having to swap in and out cartridges.
Disadvantages are:
-You need to wait for games to download (which isn't very long)
-If your MicroSD/SD card breaks, there goes your games (but you can redownload them or even back up the files on beforehand)
-There is a finite amount of games you can store. I recommend getting at least 16gb or more.
I personally rather download games because I often misplace things. Also, with downloaded games I can back up all my data onto a computer.