Under my:

C:\Documents and Settings\<user name>\My Documents\Electronic Arts\The Sims 3

Are 4 cache files (with the helper monkey icon). I'm under the assumption that those are the cache files I'm supposed to delete since ambitions came out. When ever I play the game again they keep coming back. Is this bad?

They're meant to come back. A cache file is a file that holds some of the data used by the game, like how the outfits of various sims are put together, so that the game doesn't have to figure it all out from scratch again whenever it starts up. When you clear the caches, the game regenerates all that data (thereby getting rid of any issues caused by mistakes in the cached data), and remakes the cache files.

but in order to install a mod i have to have them deleted?

Not necessarily, but deleting them is seldom a bad idea. They'll be recreated by the game as needed.

Also, you're replying to a nearly 6-year-old post.

IIRC The idea behind deleting caches after installing (or removing) a mod is so that data in the cache will not conflict with the presence (or absence) of the mod. It's primarily a precaution.