It's the service used on iOS devices (and OS X computers - Macs) to do a bunch of different things. It syncs your contacts or reminders or notes or photos or passwords or various files and other things across your devices. It's used to back up your iOS devices. It makes any content you've purchased from the Apple stores (music, apps, etc.) available to download to different devices whenever you want to. It's used to find your devices or remotely do things with them if they are lost or stolen.
It mostly functions in the background without you actually having to do things with iCloud (i.e. without you having to go to your iCloud account to move things around or whatever) other than to set up your account in the beginning and switching which functions (e.g. backing up or syncing particular things) you want on or off, and occasionally having to enter your password to log in - e.g., if you're setting up a new device or logged out of your account on a given device for some reason.
It sounds as though you're using (or have at some point used) iCloud to back up your iPhone(?). You can back it up that way or you can still, if you want, back it up to an old-fashioned computer. You can manually back it up to iCloud or have it set so that it automatically backs up whenever you plug it in to charge (and have Wifi) connection. You may have a lot of content on your iPhone (e.g. photos, mail, documents from various apps) that is using up most of your iCloud storage. Or you may be using multiple devices with the same account and that's using up more backup storage space. If storage space is an issue, you can go into your settings and see what is using up so much space.
