ITunes.iCloud. How to delete on iPhone?

Ok so I don't want some songs on my iTunes library on my iPhone. I deleted them and they are still on my iCloud, when I try to delete them, it says archive, so where will that put the songs, and does the iCloud music take up space on my iPhone? Thanks.

When you buy a song on iTunes, it keeps a record of your purchase in the cloud, so you don't have to pay again if you want to download it. When syncing your iPhone, go to the iPhone info page, and then check the box that says "Manually manage music and videos"