A Texture is a picture file that is "wrapped" around a MDL0 or is displayed raw in game to give more aesthetic appearance.
Custom textures can be illicitly added to elements in the game, such as fighters, items, assist trophies, and stage elements. This is commonly known as texture hacking or texture modding.
Custom textures (and associated custom vertex modifications) for fighters are sometimes called costumes.
Adding custom fighter textures
You must use the File Patch Code for this method to work.
Custom character textures can be downloaded from the Kitty Corps Meow Mix website Brawl Vault.
Costumes for fighters are commonly found in .pac (uncompressed) and .pcs (compressed) format. It is not always necessary to have both the .pac and .pcs files to use the costume, but having both is preferred.
To apply the costume, the .pac and .pcs files must be placed on your SD card in the appropriate folder for each fighter. See The File Placing and Naming Guide for a detailed explanation of how to name each file, and which folder to place it in.
After placing the files in the appropriate folder, CSPs can be modded into the character selection screen to match the costume you are using.
I downloaded the .zip file from Brawl Vault and extracted the files into the appropriate folder but the character doesn't look any different.
If you aren't using the File Patch Code, this method will not work.
Make sure the files are named appropriately. Files from the vault often come with filenames that are less ambiguous, but they must be renamed to a specific filename to work properly. See The File Placing and Naming Guide for these specific filenames.
Make sure the number for your texture filename matches the costume you want to replace. Take note that there is no standardized order for these numbers. For example, Link's red team costume is FitLink01, but Mario's is FitMario00 since Mario uses his default color scheme for the red team.
The custom texture doesn't work properly in All-Star Mode or Subspace Emissary.
This likely arises when you don't have matching .pac and .pcs files for the costume. If you do have both files, sometimes they are labeled incorrectly. Since the .pcs file is supposed to be compressed, there should be a noticeable difference in filesize between the two. If you got a texture from Brawl Vault with both a .pac and .pcs and they are the same filesize, whoever made the texture did it wrong.