It removes the iCloud data. If you sign back in with a new ID you will be creating a new, empty, iCloud account. You can migrate much of the data to the new account, but cannot move your existing iCloud email account or photo stream. If you want to do this, start by saving any my photo stream photos that you want to keep to your camera roll (unless already there) by opening your my photo stream album, tapping Select, tapping the photos, tap the share icon (box with upward facing arrow), then tapping Save Image (or Save to Camera Roll if you aren’t running iOS 8). If you are syncing notes with iCloud that you want to keep, you'll need to open each of your notes and email them to yourself so you can later copy and paste the text into new notes created in your new account. Then go to Settings>iCloud, tap Sign Out, choose Keep on My iPhone and provide the password to turn off Find My iPhone when prompted. Then sign back in with a different Apple ID to create your new account and choose Merge to upload the data to the new account.
If you only changed the email address associated with your existing ID you don't need to do all this. If that's the case, all you need to do is save your photo stream photos to your camera roll, then sign out of the existing account, choosing Delete from My iPhone and providing your password, then sign back in with the revised ID. Your data will download back to your phone when you sign back in.