What is a Resource Pack?
The release of "Minecraft" version 1.6 implemented the Resource Pack feature. Prior to this it was necessary to actually modify the Minecraft.jar file if you wanted to change anything substantial about the game. These packs consolidate all allowed game alterations into individual files that can be toggled on and off from an in-game dialog.
Where Can I Find Them?
Since Resource Packs are user created and distributed, the best place to look is on "Minecraft" community sites. There are a few that have sprung up since patch 1.6 catering entirely to Resource Pack rating and archiving. You can also find a great deal of support documentation in the official "Minecraft" forums should you be inclined to make your own. Generally, this will take significantly longer, but it does allow for a more unique option.
Why Should I Bother?
Some Resource Packs, particularly those that center around sound effect changes, are purely for novelty purposes. People enjoy throwing in familiar sound effects from their other favorite games. In other cases, you might want a more distinct way to hear when events are happening around you. The game already does a fair job of letting you know when danger is near, but sometimes every advantage is handy. It's all about what you want out of your game, in the end.
Found One, Now What?
Once you decide on a pack to use, you just have to drop it in the right place. The "/.minecraft/resourcepacks" folder is located in the Windows appdata directory, the Mac Library's Application Support folder, and the Linux user's Home folder. Once the archive is in this folder it will be recognized by the game and made available for selection in the Options menu.